Alfred wants to become a member of an online discussion forum. The website requires him to create a password. The password must consist of 5 characters, of which 3 must be letters and 2 must be digits. The first character of the password must be a letter. Also, repetition of the same letter in the password is not permitted but repetition of digits is permitted. How many possible ways can Alfred create the password?
So I know the answer is 9,360,000 but I got 18,720,000. This is because I thought the partition is 4! / (2! * 1! * 1!) but apparently the partition is 4! / (2! * 2!) and this confuses me. I thought that since the letters can't be repeated, we'd put one unique letter in one group, the other unique letter in the other group, and the two repeated digits in the last group. Can somebody explain this to me?

Answers

Answer 1

Answer:

Alfred can create the password in 9,360,000 possible ways

Step-by-step explanation:

Given the data in the questions;

Password of five characters must contain; three letters and 2 digits

[][][][][]

Now, using the five boxes above which as to be filled with three letters and two digits, such that; The first character of the password must be a letter and  repetition of the same letter in the password is not allowed while repetition of digits is allowed.

Now,

we know that there are 26 alphabets in English language, so the first box can be filled in 26 ways { must be a letter }

next four will be filed with two letters and two digits

so two boxes from the four can be chosen in the following ways;

⇒ ⁴C₂ = 4! / ( 2!(4-2)! = 24 / 4 = 6  { ways }

now for each choice, we can fill the chosen two boxes with letters in;

⇒ 25 × 24 = 600 { ways}

and the next two by digits; ( 0, 1, 2, ..... 9)

⇒ 10 × 10 = 100 { ways }

So in total, the possible number of ways he can create a password is;

⇒ 26 × 6 × 600 × 100

= 9,360,000 possible ways

Therefore, Alfred can create the password in 9,360,000 possible ways


Related Questions

Janet plants 20 varieties of flowers in the spring She reports that 90% of flowers she planted have bloomed .

How many varieties have bloomed

Answers

Answer:

18 varieties

Step-by-step explanation:

Total varieties of flowers that she planted = 20

100% = 20

1% = 20 ÷ 100 = 0.20

90% = 0.20 x 90 = 18

Answer:

18 flower varieties have bloomed.

Step-by-step explanation:

Select the statement(s) that is true:

a. 8 + 4 = 4( 2+ 1)

b. 2( 5 + 7) = 10+ 14

c. 8(7) = 8 ( 5+2)

d. 8 (7) = 8 ( 6 + 1)

Answers

Answer:

Use photo math, it will tell you it they are true or not

Answer: B & C & D if you look at it, it going to be the same answer.

1. B is 5+7=12 2x12=24 and 10+14=24

2. C is 8x7=56 and 5+2=7 that is 7x8=5

3. D is 8x7=56 and 6+1=7 8x7=56

So all three of that is true because it the same answer. Hope you understand

Step-by-step explanation: Hope this help :D

What note receives one beat in 2/4?

Answers

answer: a quarter note

Calculate the number of fluid ounces in 7 cups.

Answers

There are 56 fluid ounces in 7 cup

Plsss I need help it’s due today at 2:00 I’ll reward brainiest it’s super easy

Answers

Answer:

1/3

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

2/3 * 1/2 = 1/3

Which one shows the closest distance that the tip of the hand travels from 12 to 4

Answers

Answer:

if you want the answer us photo math I think !

Functions:

In image 1: Evaluate the functions

In image 2: Given the functions, find their inverse, if possible and if not possible, redefine Domain or Range

Answers

Answer:

Image 1

1. x = 4

f(4) = (- 3*4 + 1) / 6 = -11/6

2. x = -2/3

f(-2/3) = -3*(-2/3) + 10 = 2 + 10 = 12

3. x = -5

f(-5) = [tex]\sqrt{-(-5)/20}[/tex] = [tex]\sqrt{5/20}[/tex] = [tex]\sqrt{1/4}[/tex] = 1/2Image 2To work out the inverse, substitute f(x) with x and x with y, then solve for y. The new function is the inverse of the given.

1. f(x) = 5x + 3

x = 5y + 3 ⇒ 5y = x - 3 ⇒ y = (x - 3)/5f⁻¹(x) =  (x - 3)/5

2. f(x) = 4/5x

x = 4/5y ⇒ y = 5/4xf⁻¹(x) = 5/4x

3. f(x) = (2x + 7)/4

x = (2y + 7)/4 ⇒ 2y + 7 = 4x ⇒ 2y = 4x - 7 ⇒ y = 2x - 3.5f⁻¹(x) = 2x - 3.5

4. f(x) = (2x + 7) /(x + 3) = 2 + 1/(x + 3)

x = 2 +  1/(y + 3) ⇒ x - 2 = 1/(y + 3) ⇒ y + 3 = 1/(x - 2) ⇒ y = (1 - 3x + 6)/(x - 2) ⇒ y = (7 - 3x)/(x - 2)f⁻¹(x) =  (7 - 3x)/(x - 2)

5. f(x) = [tex]\sqrt{x - 4}[/tex]

x = [tex]\sqrt{y - 4}[/tex] ⇒ x² = y - 4 ⇒ y = x² + 4f⁻¹(x) = x² + 4

Which set of points on the graph represents equivalent ratios?
70
60
F
50
40
30
.
20
10
1
2 3
4
5
6 7
Х
points C, D, and F
O points B, C, and D
points B, C, and F
O points A, C, and D
Ο Ο Ο

Answers

Answer:

C or otherwise BCD

Step-by-step explanation:

right on edge

If f(x)=3x-1 and g(x)=x2+2 what is f[g(x)]

Answers

Answer:

Value of f[g(x)] = 3x² + 5

Step-by-step explanation:

Given:

f(x) = 3x - 1

g(x) = x² + 2

Find:

Value of f[g(x)]

Computation:

f(x) = 3x - 1

g(x) = x² + 2

So,

f[g(x)] = 3(x² + 2) - 1

f[g(x)] = 3x² + 6 - 1

Value of f[g(x)] = 3x² + 5

help plsssss importantt...............

Answers

Hey! So i just answered on that other one!! I’m sorry that guy wasted your points:(( check your notifs my answer should be there :)

Wayne plans to make a nut mixture in the weight ratio 1:2:5, containing cashows, almonds, and pecans, respectively. Which situation represents the function f() = 2p?


O the number of pounds of almonds Wayne needs, if he plans to use p pounds of cashews
O the number of pounds of cashews Wayne needs, if he plans to use p pounds of almonds
O the number of pounds of almonds Wayne needs, if he plans to use p pounds of pecans
O the number of pounds of pecans Wayne needs, if he plans to use p pounds of almonds​

Answers

Answer:

the number of pounds of cashews Wayne needs, if he plans to use p pounds of almonds

Step-by-step explanation:

Ration of Almonds:cashows = 1:2

Almonds/cashows = 1/2

2Almonds = cashows

f() = 2p <--> cashows = 2Almonds

As a result, the function represents the number of pounds of cashews Wayne needs, if he plans to use p pounds of almonds

What is the area of the shape below? 6 yd 5 yd 4 yd 9 yd V​

Answers

Answer:24

Step-by-step explanation:

2) Find the area. * 12 ft 12 ft​

Answers

Answer:

the answer is 144

Step-by-step explanation:

just multiply 12 by 12.

Answer:

144 ft.

Step-by-step explanation:

It is 12 x 12 which is 144 so it is 144 ft.

How was Franklin D. Roosevelt a lasting impact even on today's society​

Answers

Answer:

Franklin Delano Roosevelt, often referred to by his initials FDR, was an American politician who served as the 32nd president of the United States from 1933 until his death in 1945. A member of the Democratic Party, he won a record four presidential elections and became a central figure in world events during the first half of the 20th century. Roosevelt directed the federal government during most of the Great Depression, implementing his New Deal domestic agenda in response to the worst economic crisis in U.S. history. As a dominant leader of his party, he built the New Deal Coalition, which defined modern liberalism in the United States throughout the middle third of the 20th century. His third and fourth terms were dominated by World War II, which ended shortly after he died in office.

Step-by-step explanation:

to this ‘Great Man Theory’ it can be said that Franklin Delano Roosevelt upheld his victorious and highly regarded government through means of social, economic and political reforms, as well as ambitious personal and strategic decisions that have successfully remained influential to American society today and maintained his image as a prominent historic leader.

A shopkeeper marks the price of his goods 20%
above the purchase price but allows 10% discount to
his customers. He earns a profit of Rs. 120 to do so.
What was the actual purchase price of the goods?​

Answers

Hope this helps can I have brainlest plzz

8 Jacob wrote the expression shown.
10:5+ 4(72-6)
What do these parentheses indicate in the expression?
F.Divide 10 by 5 before adding 4
G.Multiply 4 by 72 before subtracting 6
H.Add 5 and 4 together before subtracting 6 from 72
J.Subtract 6 from 72 before multiplying by 4

Answers

You can download answer here

tinyurl.com/wpazsebu

Quadrilateral GHIJ is dilated by a scale factor of 22 to form quadrilateral G'H'I'J'. What is the measure of side H'I'?

Answers

Answer:

[tex]H'I = 48[/tex]

Step-by-step explanation:

Given

See attachment for complete question.

From the attachment, we have:

[tex]GH=16.5[/tex]

[tex]HI =24[/tex]

[tex]IJ = 17[/tex]

[tex]JG =32.2[/tex]

[tex]k = 2[/tex] --- Scale factor

Required

Find H'I

The corresponding side of H'I is HI.

So:

H'I is calculated as:

[tex]H'I = k * HI[/tex]

This gives:

[tex]H'I = 2 * 24[/tex]

[tex]H'I = 48[/tex]

Answer I to j is 42

Step-by-step explanation:

the first one help please asap, i will mark as brainliest

Answers

Answer:

They originally paid $28,750

Source:

Trust me bro, I used a calculator

59,000-1500= 57,500/2=28,750

3(6x)-8x = -2+5 (2x+1)

Answers

Answer:

x = 3

Step-by-step explanation:

So you will distribute the number beside the ( )

so the equation be looking like :

18x - 8x = 10x + 5 - 2

now combine like terms

18x - 8x = 10x

5 - 2 = 3

10x = 10x +3

now subtract 10x to the other side they cross off

leaving x = 3

and so that's your answer

hope this helps

Answer:

this question is wrong i think

can you help me with 1 - 4

Answers

Me das mas información porfavor?

BRAINLIEST ANSWER ☘️

order the numbers from least to greatest

0.222

0.18

0.1

0.24

0.21

Answers

Answer:

0.1, 0.18, 0.21, 0.222, 0.24

Explanation:

look at the first number:

between 0.1 and 0.18, 0.1 is smaller therfore it is the least

next to that would be 0.18

next, 0.21, 0.222, and 0.24 all has the same first number so take a look at the second number:

0.21 would be the third number since the second number is 1, which is the smaller number out of 3

the 4th number would be 0.222 because 0.22 is less than 0.24

lastly, the greatest or largest number would 0.24

The area of a wall to be tiled in 1.5 metres by 2.5 metres.
Tiles are 50cm by 50cm
The tiles are £0.99 each.
How much will the tiles cost in pounds

Answers

Answer:

£14.85

Step-by-step explanation:

The total number of tiles needed

= 5 × 3

= 15

∴ The total cost of the tiles

= £0.99 × 15

= £14.85

Find the value of the triangle h=?

Answers

i don’t know sorry bro sorry

Answer:

h = 7.61 ft

Step-by-step explanation:

area = 29 ft²

area = 1/2 × h × h

29 ft² = 1/2 × h × h

29 × 2 = h²

58 = h²

√58 = h

7.61 ft = h

What is the ratio of the leg opposite the angle to the leg adjacent to the
angle.

Answers

Answer:

tangent (angle) or tan (angle)

Step-by-step explanation:

tangent (angle) = the leg opposite the angle / the leg adjacent to the angle

Trever invested $10,000 in an account that earns 8.5%
interest that is compounded monthly.
(a) Write an exponential model for the balance of the
account.
(b) Determine the amount of money in the account
after 15 years.

Answers

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Trever invested $10,000 in an account that earns 8.5% interest that is compounded monthly.

First, we need to calculate the monthly interest rate:

i= 0.085 / 12= 0.00708

Now, to calculate the future value of the investment, we need to use the following formula:

FV= PV*(1+i)^n

PV= initial investment

i= interest rate

n= number of periods

In this case:

FV= 10,000*(1.00708^n)

Finally, for 15 years:

n= 15*12= 180 months

FV= 10,000*(1.00708^180)

FV= $35,605.31

Given f(x) = V(3 x – 12) +2, what is the range in set notation?

Answers

Answer:

Step-by-step explanation:

[2,∞)

Answer:

it's 2

Step-by-step explanation:

what 2-1+46-2x0

I tried O but it didn't work

Answers

Answer:

answer is 47

Step-by-step explanation:

use the rule, 2x0 = 0 then (2- 1) that's 1 and then (46-0) that's 46 so 1 + 46 is 47

PLEASE HELP AGAIN!! Max deposited $4,008 in a savings account with simple interest. Four years later, he had earned $641.28 in interest. What was the interest rate?​

Answers

Answer:

4%

Step-by-step explanation:

For simple interest, the equation is I = PRT, where I is the interest, P is the principal/amount invested, R is the rate as a decimal, not percentage, and T is time in years.

641.28 = (4008)(r)(4)

641.28 = 16,032r

r = 0.04 = 4%

Find the area of shaded part.

Answers

Answer:

13.76

Step-by-step explanation:

First you have to find the area of the square and then subtract the area of the circle from it.

A=8x8

Area of the Square is 64

[tex]a = \pi { 4}^{2} [/tex]

a= 50.24

A=64-50.25

THE FINAL AREA IS 13.76

Please help me with this

Wilbur landed his plane.
The plane's elevation relative to the ground (in meters) as a function of time (in seconds) is graphed.

A. 6 meters per second
B. 5 meters per second
C. 7 meters per second
D. 4 meters per second

Answers

Used Desmos and you’ll get your answer but do like 4m or y=4
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