Chapter 11, Problem 7CST

To determine

To calculate:the number of different combinations to choose 4 members.

Answer to Problem 7CST

the number of different combinations to choose 4 members is,

  ${}_{10}{C}_4=210$

Explanation of Solution

Given information:

The club has 10 members.

Calculation:

To calculate the number of different combinations to choose 4 members,

  $\begin{array}{l}{}_{10}{C}_4=\frac{{}_{10}{P}_4}{4!}\left[\text{use combination formula}\right]\\ {}_{10}{C}_4=\frac{10\cdot 9\cdot 8\cdot 7}{4\cdot 3\cdot 2\cdot 1}\left[{\text{write }}_{10}{P}_4\text{ and 4! as products}\right]\\ {}_{10}{C}_4=210\left[\text{divide out common factor}\right]\end{array}$

Therefore,

the number of different combinations to choose 4 members is

  ${}_{10}{C}_4=210$ .