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

1 Answer
Mar 4, 2016

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