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#