Chapter 8.4, Problem 10E

To determine

To find: the value of binomial coefficient.

Answer to Problem 10E

The value of binomial coefficient is 153.

Explanation of Solution

Given information:

Given binomial coefficient

  ${}_{18}{C}_2$

Calculation:

It states that the binomial coefficient ${}_n{C}_r$ is equal to $\frac{n!}{\left(n-r\right)!r!}$ .

We have $n$ as 18 and $r$ as 2.

Substitute the values of $n$ and $r$ in ${}_n{C}_r=\frac{n!}{\left(n-r\right)!r!}$ .

  $\begin{array}{c}{}_{18}{C}_2=\frac{18!}{\left(18-2\right)!2!}\\ =\frac{18!}{16!2!}\\ =\frac{18\cdot 17\cdot 16!}{16!2\cdot 1}\\ =153\end{array}$