Chapter 11.7, Problem 28E

To determine

To find the number of combinations of ${}_9{C}_3$

Answer to Problem 28E

The number of combinations of ${}_9{C}_3$ is 84

Explanation of Solution

Given information:

Consider the given combination ${}_9{C}_3$

Calculation:

  ${}_n{C}_r$ = ${}_9{C}_3$

  ${}_n{C}_r$ = $\frac{n!}{r!\times (n-r)!}$ [Use combinations formula]

  ${}_9{C}_3$ = $\frac{9!}{3!\times (9-3)!}$

  ${}_9{C}_3$ = $\frac{9!}{3!\times 6!}$ = $\frac{9\times 8\times 7\times 6\times 5\times 4\times 3}{3\times (6\times 5\times 4\times 3\times 2\times 1)}$ [Divide out common]

  ${}_9{C}_3$ = 84 [Simplify.]