Chapter 11.7, Problem 20E

To determine

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

Answer to Problem 20E

The number of combinations of ${}_{15}{C}_6$

Explanation of Solution

Given information:

Consider the given combination ${}_{15}{C}_6$

Calculation:

  ${}_n{C}_r$ = ${}_{15}{C}_6$

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

  ${}_{15}{C}_6$ = $\frac{15!}{6!\times (15-6)!}$

  ${}_{15}{C}_6$ = $\frac{15!}{6!\times 9!}$ = $\frac{15\times 14\times 13\times 12\times 11\times 10\times 9\times 8\times 7\times 6}{6\times (9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1)}$ [Divide out common]

  ${}_{15}{C}_6$ = 5005 [Simplify.]