Chapter 0, Problem 27PO

To determine

whether each situation involves a permutation or a combination and then find the number of possibilities.

Answer to Problem 27PO

The numbers of ways are 5200300 ways .

Explanation of Solution

Given information :

Event is given as forming a team of 12 athletes from a group of 25 who try out.

In the given event, arrangement does not matter so it is a combination.

The number of ways is given by,

  $\begin{array}{c}C{}_{12}=\frac{25!}{13!12!}\\ =\frac{25\times 24\times 23\times 22\times 21\times 20\times 19\times 18\times 17\times 16\times 15\times 14}{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}ways\\ =5200300ways\end{array}$

So, the numbers of ways are 5200300 ways .