Suppose we want to choose 5 objects, without replacement, from 9 distinct objects. (a) How many ways can this be done, if the order of the choices is not taken into consideration? (b) How many ways can this be done, if the order of the choices is taken into consideration?

The number of ways if the order of the choices is not taken into consideration and taken into consideration will be 126 and 15,120, respectively.

A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.

Suppose we want to choose 5 objects, without replacement, from 9 distinct objects.

Then the number of ways that this can be done, if the order of the choices is not taken into consideration will be given as,

⁹C₅ = 9! / [(9 - 5)! x 5!]

⁹C₅ = (9 x 8 x 7 x 6 x 5!) / (4 x 3 x 2 x 1 x 5!)

⁹C₅ = 126

Then the number of ways this can be done, if the order of the choices is taken into consideration will be given as,

⁹P₅ = 9! / [(9 - 5)!

⁹P₅ = (9 x 8 x 7 x 6 x 5 x 4!) / 4!

⁹P₅ = 15,120

The number of ways if the order of the choices is not taken into consideration and taken into consideration will be 126 and 15,120, respectively.

More about the permutation and the combination link is given below.

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