Chapter 10.5, Problem 33E

To determine

To calculate:

The groups of four golfers are possible

Answer to Problem 33E

The groups of four golfers possible are $635376$ .

Explanation of Solution

Given information:

  

Number of golfers: $n=64$

Number of golfers in group: $r=4$

Calculation:

The formula for permutation for $n$ objects taken $r$ at the time is as:

  $C{}_r=\frac{n!}{\left(n-r\right)!\cdot r!}\cdot \cdot \cdot \left(1\right)$

Where,

  $\begin{array}{l}n=64\\ r=4\end{array}$

Put the values in equation (1)

  $\begin{array}{l}C{}_4=\frac{64!}{\left(64-4\right)!\cdot 4!}\\ C{}_4=\frac{64!}{60!\cdot 4!}\\ C{}_4=\frac{64\times 63\times 62\times 61\times 60!}{60!\times 4\times 3\times 2\times 1}\\ C{}_4=\frac{64\times 63\times 62\times 61}{4\times 3\times 2\times 1}\\ C{}_4=635376\end{array}$

Hence, the groups of four golfers possible are $635376$ .