Chapter 13.1, Problem 36E

To determine

To calculate: The value of expression $C\left(14,7\right)$ .

Answer to Problem 36E

The value of expression $C\left(14,7\right)$ is $3432$ .

Explanation of Solution

Given information:

The expression $C\left(14,7\right)$ .

Formula used:

If there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Calculation:

Consider the expression $C\left(14,7\right)$ .

Recall that if there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Here n is 14 and r is 7.

  $\begin{array}{c}C\left(14,7\right)=\frac{14!}{7!\left(14-7\right)!}\\ =\frac{14\cdot 13\cdot 12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7!}{\left(7\cdot 6\cdot 5\cdot 4\cdot 3\cdot 2\cdot 1\right)\left(7!\right)}\\ =3432\end{array}$

Thus, the value of expression $C\left(14,7\right)$ is $3432$ .