Chapter 12.7, Problem 49STP

To determine

To find: The no. of ways $5$ -player groups can the coach choose to play during a game.

Answer to Problem 49STP

The no. of ways $5$ -player groups that can the coach choose to play during a game are $462$ .

Explanation of Solution

Given:

The given information is:

A basketball team has 11 players.

Calculation:

As in order to choose $5$ -player out of 11 players, there is no need of order of the players so here combination will be used.

The calculation is given as:

  $\begin{array}{c}C{}_r=\frac{n!}{r!\left(n-r\right)!}\\ C{}_5=\frac{11!}{5!\left(6\right)!}\\ =\frac{11\cdot 10\cdot 9\cdot 8\cdot 7}{5\cdot 4\cdot 3\cdot 2\cdot 1}\\ =462\end{array}$

Therefore the no. of ways $5$ -player groups that can the coach choose to play during a game are $462$ .