Chapter 13.1, Problem 1CFU

To determine

To find: The comparison and the contrast for the permutation and combination.

Answer to Problem 1CFU

The comparison and the contrast for the permutation and combination.

Explanation of Solution

Consider the formula for the number of permutation of n subjects taken all at one time is,

  $P\left(n,n\right)=n!$

Consider the permutation of the n object taken $r$ at a time is,

  $P\left(n,R\right)=\frac{n!}{\left(n-r\right)!}$

Consider that the combination is the selection of the object and the order is not a consideration here. The formula for the $n$ objects taken $r$ time is obtained by dividing the number of permutations by the number of arrangements that contains the same elements.

Thus, the number of combination of the $n$ objects taken $r$ time is defined as,

  $C\left(n,r\right)=\frac{n!}{\left(n-r\right)!}$