Question

How do you find the number of permutations of 5 CDs if you have a total of 23 CDs?

Answer 1

`4037880`

Explanation:

A permutation is an ordered arrangement of all part of a set of items. In permutations that is with arrangements of the objects, the order of elements is taken consideration.

For example, the number of permutations of `n` different objects taken `r` at a time is `nPr`, in which;

`"^(n)P_r=(n!)/((n-r)!)`

`=n(n-1)(n-2)...{n-(r-1)}`

(Note that `n! =nxx(n-1)xx(n-2)xx...xx2xx1`)

Given a total of `23` CDs, assuming that each CD is different, taken only `5` CDs at a time is given by;

`"^(23)P_5=`

`=(23!)/((23-5)!)`

`=(23!)/(18!)`

`=(23xx22xx21xx20xx19xxcancel(18!))/cancel(18!)`

`=4037880`