Chapter 12.4, Problem 33PPS

To determine

To find: the combination that different groups of players could be selected.

Answer to Problem 33PPS

The number of different groups of players that the coach had to select is 792.

Explanation of Solution

Given information:

Total number of players is 12.

Total number of selected players to make the different group is 5.

Formula used :

  $c(n,r)=\frac{n!}{(n-r)!r!}$

Calculation:

Number of different groups of players that could be selected are-

  $\begin{array}{l}c(n,r)=\frac{n!}{(n-r)!r!}\\ c(12,5)=\frac{12!}{(12-5)!5!}\left[\text{Since }n=12\text{ and }r=5\right]\\ =\frac{12!}{7!5!}\\ =\frac{12\times 11\times 10\times 9\times 8\times 7!}{5\times 4\times 3\times 2\times 1\times 7!}\left[\text{Divide by common factor}\text{.}\right]\\ =792\end{array}$

Hence, there are 792 different groups of players that the coach had to select.