Assuming n is a natural number greater than 1, how many unique positions of n identical rooks on an n by n chessboard exists, such that exactly one pair of rooks can attack each other? [Hint: How many empty rows or columns will there be?]

Answers

Answer 1

The total number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other is (n - 1)^2 * (n - 1)! or (n - 1) * (n - 1)! * (n - 1).

To find the number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other, we need to consider the number of empty rows and columns.

First, let's consider the number of empty rows. Since exactly one pair of rooks can attack each other, we know that there can be at most one rook in each row. This means that there are n rows with at most one rook each, leaving (n - 1) empty rows.

Next, let's consider the number of empty columns. Again, since exactly one pair of rooks can attack each other, there can be at most one rook in each column. This means that there are n columns with at most one rook each, leaving (n - 1) empty columns.

Now, we can use combinations to find the number of ways to choose one row and one column for the pair of rooks that can attack each other. There are (n - 1) options for the row and (n - 1) options for the column, giving us a total of (n - 1) * (n - 1) = (n - 1)^2 possible combinations.

Finally, we need to multiply this by the number of ways to place the remaining rooks in the empty rows and columns. Since each rook can be placed in any of the empty rows or columns, there are (n - 1)! ways to arrange the remaining rooks.

Therefore, the total number of unique positions of n identical rooks on an n by n chessboard such that exactly one pair of rooks can attack each other is (n - 1)^2 * (n - 1)! or (n - 1) * (n - 1)! * (n - 1).

To know more about combinations refer here :

https://brainly.com/question/30648446#

#SPJ11


Related Questions

Last year, Michael opened an investment account with $5400. At the end of the year, the amount in the account had decreased by 23.5%. How much is this
decrease in dollars? How much money was in his account at the end of last year

Answers

He would have $4131 left from $5400 with a decrease with 23.5%

PLEASE HELP I WILL MARK BRAINLIEST

name 2 rights of someone accused of a crime that you observe in the pic above.
A. right to a trial and lawyer
B. right to a lawyer and providing evidence
C. Trial with a judge and witness
D. Right to take notes and provide evidence for defence ​

Answers

Answer:

it is b the right to evidence lawyer.

Answer:

B. right to lawyer and providing evidence

Step-by-step explanation:

What is the vertex form of 3x^2+6x+10

Answers

3x² + 6x + 10

= 3(x+1)² + 7

Vertex (h,k)
= (-1,7)

Answer:

3x2+6x−10

y=3x2+6x−10

Rewrite the equation in vertex form.

y=3(x+1)2−13

Use the vertex form, y=a(x-h)2+k, to determine the values of a h, and k.a=3h=−1k=−13 (h,k).(−1,13)

Step-by-step explanation:

can someone help me with these three? I just need to find the unit rates for all, I’ll mark as brainliest!!

Answers

Answer:

6. 7.5/1

7. 2.4/1

8. 40/1

Step-by-step explanation:

All you have to do is divide the 2 numbers to find the unit rate.

Answer:

6: 7.5 pizzas per Classroom

7: 2.4 Liters per test

8: 40 Points per Game

A baker needs 4 3⁄4 cups of flour. If she uses a 1 1⁄2 cup measuring scoop, how many scoops of flour must the baker use to have at least 4 3⁄4 cups?(must be a whole number)

Answers

Answer:

If you did it three times it would be 4 1/2. If you wanted to make it at least 4 3/4 then you would need to do 1 1/2 4 times.

Step-by-step explanation:

-6x-7-4x-2 How can I solve this?

Answers

Use the distributive property method

Use PEMDAS

Parentheses first

Exponents next

Multiplication then

Division in the same step

Addition then

Subtraction

The correct answer is 10x-9

HELP QUICK whats the domain and range of g(x)=√x-3+5

Answers

Answer:

check it..

Step-by-step explanation:

domain and range...

12x + 15y = 9
−12x − 18y = −6
HELP JUST SOLVE IT

Answers

Solve for the first variable in one of the equations, then substitute the result into the other equation.
Point Form:
(2, -1)

Equation Form:
x= 2, y= -1

Answer:

x = 2, y = -1

Step-by-step explanation:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

12x+15y=9,−12x−18y=−6

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

12x+15y=9

Subtract 15y from both sides of the equation.

12x=−15y+9

Divide both sides by 12.

x=  1/12 (−15y+9)

Multiply 1/12 ​ times −15y+9.

x = -5/4y+3/4

Substitute -5y+3/4 for x in te other equation, -12x - 18y = -6

-12 ( -5/4y+3/4) -18y = -6

Multiply −12 times -5y +3/4

15y−9−18y=−6

Add 15y to −18y.

−3y−9=−6

Add 9 to both sides of the equation.

−3y=3

Divide both sides by −3.

y=−1

Substitute −1 for y in x= -5/4y+3/4. Because the resulting equation contains only one variable, you can solve for x directly.

x= -5/4(-1)+3/4

Multiply -5/4 times -1.

x = 5+3/4

Add 3/4 to 5/4 by finding a common denominator and adding the numerators. Then reduce the fraction to lowest terms if possible.

x=2

The system is solved.

I need help on this

Answers

Answer:

(1,0)

Step-by-step explanation:

Subtract the x's and y's from eachother than divide this by two. Add this number onto the lowest of the x and ys and you get the midpoint. The same as fining the middle of two numbers but you are dealing with 2 pairs of numbers

În desen este reprezentat trapezul
ABCD și O punctul de intersecție a di-
agonalelor AC și BD. Completați case-
ta, astfel încât să obțineți o propoziţie
adevărată:
Dacă aria triunghiului DOA este egală
cu 20 cm², atunci aria triunghiului COB
este egală cu​

Answers

Answer:

ab hyppotenusejabqianahqiwnna. jajabanqk

7. What is the area of the trapezoid shown? 4 cm 10 cm 8 cm W 10 cm​

Answers

Answer:

88 ... .... . ... . . . ... ............... ....


Given a sphere with a radius of 2 cm find its volume to the nearest whole number.

A 17 cm

B.3cm

C. 33 cm

D. 3 cm

Answers

D for sure it is Bc the whole number

What is the surface area?
5 mm
4 mm
5 mm
6 mm
7 mm
square millimeters

Answers

Answer:

Base of 5mm, Height of 6mm, Width of 7mm214mm^2

Base of 4mm, Height of 4mm, Width of 10mm192mm^2

Base of 5mm, Height of 6mm, Width of 7mm214mm^2

Base of 6mm, Height of 3mm, Width of 2mm72mm^2

7mmLittle over 1/4 Inch0.27559 Inches

The total surface area is 124 square millimeters.

What the surface area of a rotating prism?

To find the surface area of any kind of prism we use the general formula. The total surface area of a prism is the sum of lateral surface area and area of two flat bases.

The total surface area of a Prism = (2 × Base Area) + (Base perimeter × Length).

Here, area of base is Area=2(Base×Height)

= 2(6×4)

= 12 square millimeters

Now, Base perimeter × Length= (5+5+6)×7

= 16×7

= 112 square millimeters

Total area = 12+112

= 124 square millimeters

Therefore, the total surface area is 124 square millimeters.

To learn more about the surface area of a prism visit:

https://brainly.com/question/28016184.

#SPJ2

Write your own algebraic expression with atleast four terms that can simplify to 12x+4 (PLEASE HELP ASAP)​

Answers

Answer:

4(2x + 1) + 4x   =   8x + 4 + 4x   =   12x + 4

What is the slope of the line shown?

A. slope = 3
B. slope = 1/2
C. slope = 2
D. slope = -3

Answers

i think it’s 1/2, you have to count the rise over run from a point to the next, so it would go one up and then two over

Answer:

The answer is B - 1/2.

Step-by-step explanation:

Rise over run tells you the slope. You take two points (in this it's (0,-3) and (6,0)) and you see how many units it takes to be on the same y line as the other point. Then you do the same for the x line. You divide the rise (y line) by the run (x line) and that's your slope.

How do you simplify 14.938 - 14.93 ?

Please help

Answers

Answer:

0.008

Step-by-step explanation:

To know the steps pls look at the pic above

HELPPP ME PLEASEEE!!!!

Answers

You need a common denominator in your case 2x4=8 ( because those are the demoninators) then 1x2=2 and 2x4=8 8/8 2/4 meaning it’s one half

Solve for x. Round your answer to the nearest tenth.
9.2
X
16.5

Answers

Answer:

152

Step-by-step explanation:

On Monday, Florencia's hair was h centimeters long. She got a haircut on Tuesday, so her hair was only 75% percent of the length it was on Monday.
Which expressions could represent how many centimeters long Florencia's hair was after the haircut?
(The Question says to pick 2 answers out of the multiple choice options so here you go)
A. h (1-0.75)
B.(1- 75/100) h
C. 3/4 h
D. 0.75 h
E. 1/4 h

Answers

Answer:

D

Step-by-step explanation:

75/100 = .75 x the Monday length (h)

in integers how to know if minus (-) 1 upon 2 is greater or minus (-) 1 is greater???​

Answers

Answer:

1/2 is 0.5 so -1/2=-0.5

-0.5 is greater than -1

use a number line

Step-by-step explanation:

By looking at the number line we can easily tell which integers are greater (larger) than a certain number and which are less (smaller) than the number. When two numbers are located on a number line, the number to the right is larger than the number to the left. –1 is less than –1/2 because it is to the left of –1/2.

(Please heart the answer if you find it helpful, it's a motivation for me to help more people)

So like I need help on this,

Choose the graph that represents the figure and classify it. Then find the area.


D(-1, -1), E(-1, 3), F(2, 4), G(2, -3)

Answers

Answer:

Trapezoid with the area 16.5 unit²

Step-by-step explanation:

Plotted the given points to find out the figure is trapezoid.

Area formula for trapezoid:

A = 1/2(b₁ + b₂)h

The length of the bases:

b₁ = DE = 3 - (-1) = 4b₂ = FG = 4 - (-3) = 7

h is the horizontal distance between the bases:

h = 2 - (-1) = 3

The area is:

A = 1/2(4 + 7)(3) = 16.5 unit²

write an expression for the perimeter of the triangle shown below 2.3x + 14 2x -0.2x + 15

Answers

Answer:

4.1x + 29

Step-by-step explanation:

So the perimeter would be the sum of all of the sides, so:

[tex]2.3x + 14 + 2x - 0.2x + 15\\= 4.1x + 29[/tex]

Answer: 4.5x+ 29 which is 3, so 3 is correct.

Step-by-step explanation:

P = a+b+c

First do the ordered pairs ( add the numbers with the x to the end, then add the other numbers with no x's)

Alek gives 18 flowers to each person at his office, There are 42 people at his office. How many flowers does alek give away?

Answers

Answer:

he gives away 756 flowers

Step-by-step explanation:

18*42=756

BRAINLIEST to wherever gets this correct ​

Answers

Answer:

[tex]300\pi[/tex] cubic feet

Step-by-step explanation:

Let r be the radius of cone and h be the height of cone.

Radius of cylinder=r

Height of cylinder=h

Volume of cone=[tex]100\pi ft^3[/tex]

We have to find the volume of cylinder.

We know that

Volume of cone=[tex]\frac{1}{3}\pi r^2 h[/tex]

[tex]100\pi=\frac{1}{3}\pi r^2 h[/tex]

[tex]r^2 h=300[/tex]

Volume of cylinder=[tex]\pi r^2 h[/tex]

Using the formula

Volume of cylinder=[tex]\pi (300)=300\pi ft^3[/tex]

Hence, the volume of cylinder=[tex]300\pi[/tex] cubic feet

HELPPP PLEASEEEEEEE I NEED HELP

Answers

Answer:

Part A:   -3x^8 + 2x^5 + 4x^3

Part B:   8

Part C:   3

Part D:   -3x^8

Part E:   -3

Step-by-step explanation:

A. Standard polynomial is :

[tex] - 3 {x}^{8} + 2 {x}^{5} + 4 {x}^{3} [/tex]

B. Degree of the polynomial is : 8

C. Number of terms are : 3

D. Leading term of the polynomial is:

[tex]-3 {x}^{8} [/tex]

E. Leading co effecient of the polynomial is: -3

That's not an answer for me

Answers

Answer:

so you need a answer or a question

Answer:

child anywaysssss

Step-by-step explanation:

yfgxgx

Select the correct answer. Which equation describes the line graphed above? A. y=-4x-5 B. y=-1/5x-4 C. y=-5x-4 D. y=-4x-1/5

Answers

Answer:

Option B

Step-by-step explanation:

Answer: B.

Step-by-step explanation: Plato

A measure of how much space something takes up ?

Answers

Answer:

Volume

Step-by-step explanation:

Mass is measured using a scale. Volume is the amount of space matter takes up. Volume can be measured by multiplying the length, width, and height of an object, or by using a measuring cup and seeing how the measurement of water changes in a cup. Density is the amount of matter an object has in a certain space.

Answer:

VOLUME

Step-by-step explanation:

PLSSSS HELP IM BEGGING YOU PLSSSS

Answers

92000 in expanded form
9.2 x 10^4 in scientific notations
Simplify 10^4 to 10,000 and 10^3 to 1,000:
9 x 10,000 + 2 x 1,000

Simplify 9 x 10,000 and 2 x 1,000:
90,000 + 2,000

= 92,000

One morning, the thermometer read -14 fahrenheit. By noon, the temperature had risen 12 degrees. What was the temperature at noon?

Answers

Answer:

-2 degrees

Step-by-step explanation:

-14 + 12 = -2

Other Questions
an exchange system which has occasional government intervention is a Lots of things require balance: riding a bike, walking a balance beam, jumping rope. Losing balance can cause us to get hurt. The same is true for living things. Plants and animals must maintain an internal balance to stay healthy. Living things have internal communication systems that help to keep things in homeostasis or balance. A stimulus is any change in an organisms environment that causes the organism to react. The change can be internal or external. For example, when you get hot, you move to the shade. The heat is an external stimulus and moving to the response is the response you make to cool off or come back to homeostasis. If you get hungry, you eat a snack. The hunger is an internal stimulus. Eating a snack is your response.Which of these is a response to an external stimuli? Select ALL that apply.A.) hibernationB.) phototropismC.) wiltingD.) thirstE.) dormancy Consider a transfer function H (W) = 1+j2 where wo =660 wo rad/sec. Calculate the frequency in Hertz at which the phase of the transfer function is -45 degrees. which of the following terms is a hardened computer specifically designed to resist and oppose illicit or unwated attempts at entry How many units must be sold if contribution margin is 20, fixed costs are $5,000 and profits are $25,000? O 10,500 units O 1,500 units 2,000 units 0 2,500 units Part A Calcium oxide reacts with water in a combination reaction to produce calcium hydroxide: CaO (s) + H2O (1) + Ca(OH)2 (s) In a particular experiment, a 3.50-g sample of CaO is reacted with excess water and 4.12 g of Ca(OH)2 is recovered. What is the percent yield in this experiment? 1.18 84.9 5.04 89.2 118 Submit Request Answer You will need to know that Force (N) is equal to mass (kg) multiplied by acceleration (m/s2) for this problem. A fearless space explorer has discovered a new planet with a frictionless surface! He pushes a large crate with a mass of 220kg a distance of 5.3 km, as he does so, it accelerates at a rate of 2m/s2. How much work has our intrepid hero done? Select all of the options that correspond to possible bootstrap samples from the following sample values: -8, -3, 13, 2, 15 -3,-8, 13, 2, 2 0 -3, 13, -8, -8,-3, 31, 14, -2 -8, -8, -8,-8, -8 15, 2, 15, 2, -3 koepka corp. has a project with the following cash flows: yearcash flow 0 $35,400 1 26,600 2 29,400 reentrant code is easier to share when paging is used, because generally if a firm becomes less risky, its share price will An SRS of 16 items is taken from Population 1 and yields an average = 253 and standard deviation s1 = 32. An SRS of 20 items is taken (independently of the first sample) from Population 2 and yields an average = 248 and a standard deviation s2 = 36. Assuming the two populations have the same variance 2 and the pooled variance estimator of 2 is used, the standard error of is: use c++ please and do not get some wrong code for meIntroductionIn this lab you will practice using basic input/output, structs, and arrays of structs. Be sure to read this lab thoroughly, especiallythe sections of Collaboration and the Hand-in Procedure.CollaborationCollaboration amongst students is allowed to the extent outlined in the syllabus. That being the case, the goal of theseassignments is not to share code, but to learn the tools you need to succeed as a computer scientist. Students are expected towrite their own code free of plagiarism from any other student past or current. All assignments will be cross referenced acrossall sections of CS135 using the Measure Of Software Similarity (Moss) to automatically determine the similarity of programs.Refer to the syllabus for further details and consequences of breaking this policy.LabTo start your lab you will need a struct to read data into. The struct definition should be placed above main() and belowusing namespace std. The struct should be called PurchaseType and contain the following fields:1. string customerID2. string productName3. double price4. int qtyPurchased5. double taxRateWrite a complete program that:1. Uses a user defined function:void openFile(ifstream& iFile, string prompt)Which gets the name of a file from the user and opens it into iFile by:a. Prompting the user for a filename using prompt and reading the filename into a string.b. Opening the file name obtained in (1a) into iFile, and verifying that it opened. If the file does not open theprogram should output an error message and continue from (1a) until a valid file name is entered. See theexample output for error formatting.i. The file contains strings, integers, and doubles with 5 values per line with 10 lines of data in the file.Each line of data represents a different item purchased by a customer.2. Creates an array of instances of the PurchaseType struct to hold the data from the file obtained in (1).3. Uses a user defined function:void readFile(ifstream& iFile, PurchaseType purchases[])Which reads the data from iFile into purchases by:a. iFile contains rows of data which correspond to the elements of the PurchaseType struct. Iterate throughiFile inserting the rows of data, using str.find() str.substr(), into purchases until eof is hit.(More steps on next page)4. Uses a user defined function:void printPurchaseData(PurchaseType purchases[], int size)Which prints the data contained in purchases by:a. Using iomanip to nicely output all the data in a tabular format. You will need to calculate the total price foreach product purchased by multiplying the price of each product by the quantity purchased, and thenmultiplying by the (tax rate + 1). See the example output for formatting.b. Keeping track of each total found and outputting the average total at the end of the table.c. Keeping track of the count of unique customers and outputting the total unique customers at the end of thetable.main() should only contain variable declarations and function calls (to your user-defined functions). All data must be readinto an array of PurchaseType structs first, then the required output. You must write all of the functions in this lab, failing todo so will result in you receiving a 0 for this lab. Failure to use an array of structs will also result in a 0 for this lab. Seethe example output for examples and formatting.Prototypes for your user defined functions are:1. void openFile(ifstream&, string);2. void readFile(ifstream&, PurchaseType[]);3. void printPurchaseData(PurchaseType[], int);Example OutputAn example of an interaction with your program is shown below, your output should match these examples exactly. (The wordsprinted in blue are from the computer, based on your commands, the words in red are user input. Note: these colors are simplyhere to distinguish components and not needed in your program.):Alexs-iMac:lab11b alex$ g++ -Wall -pedantic -Werror main.cppAlexs-iMac:lab11b alex$ ./a.outEnter file name**errorError: Invalid FileEnter file name**purchases1.csv+-------------+--------------+-------+----------+----------+-------+| Customer ID | Product Name | Price | Quantity | Tax Rate | Total |+-------------+--------------+-------+----------+----------+-------+| A134CX2 | shirt | 10.00 | 1 | 8.25 | 10.82 || A134CX2 | pants | 15.95 | 2 | 8.25 | 34.53 || A134CX2 | jacket | 24.49 | 1 | 8.25 | 26.51 || 4J37I2I | blouse | 19.99 | 1 | 8.25 | 21.64 || 4J37I2I | pants | 14.98 | 1 | 8.25 | 16.22 || 4J37I2I | mittens | 9.99 | 3 | 8.25 | 32.44 || 4J37I2I | socks | 10.98 | 3 | 8.25 | 35.66 || B834621 | gloves | 9.99 | 2 | 7.15 | 21.41 || B834621 | cap | 24.99 | 3 | 7.15 | 80.33 || 27G8ZZY | earrings | 49.99 | 1 | 8.25 | 54.11 |+-------------+--------------+-------+----------+----------+-------+Unique users: 4Average total: $33.37 question 17with respect to the progression of shin-byung, which of the following actions by the patient would best demonstrate high self-efficacy? TRUE/FALSE.Disparate-treatment discrimination occurs when a protected group of people is adversely affected by an employers practices, procedures, or tests even though they do not appear to be discriminatory. Drag each number to a box to complete the table. Each number may be used once or not at all.8,000533,00021,000Kilometers Meters1 2,0005,0008 Jordan is constructing the bisector of What should Jordan do for the first step? Question 1 options: Place the point of the compass on point M and draw an arc, making sure the width is greater than MN. Place the point of the compass on point M and draw an arc, making sure the width of the compass opening is less than MN. Use the straightedge to extend in both directions. Use the straightedge to draw the line that passes through point M. According to Newton's law of cooling (sec Problem 23 of Section 1.1), the temperature u(t) of an object satisfies the differential equation du/dt = -K(u - T) where T is the constant ambient temperature and k is a positive constant. Suppose that the initial temperature of the object is u(0) = u_0 Find the temperature of the object at any time. Using the Bloch theorem, show that the probability of finding an electron at a position r+R in the crystal is the same as that of finding it at a position r. Here, R is a Bravais lattice vector. to test this series for convergence [infinity] n / (n^5 + 6)n=1you could use the limit comparison test, comparing it to the series [infinity] 1 / n^pn=1where p= _____completing the test, it shows the series:a. divergesb. converges