Chapter 12, Problem 74RE

To determine

Evaluate the expression.

Answer to Problem 74RE

The evaluate value of the expression is $255$

Explanation of Solution

Given information:

It is given in the question that, the expression is $\left(\begin{array}{l}10\\ 2\end{array}\right)+\left(\begin{array}{l}10\\ 6\end{array}\right)$ .

Formula used:

  $\left(\begin{array}{l}n\\ r\end{array}\right)=\frac{n!}{r!\left(n-r\right)!}$

Calculation:

  $\left(\begin{array}{l}10\\ 2\end{array}\right)+\left(\begin{array}{l}10\\ 6\end{array}\right)$

By using the formula $\left(\begin{array}{l}n\\ r\end{array}\right)=\frac{n!}{r!\left(n-r\right)!}$

  $\begin{array}{l}\frac{10!}{2!\left(10-2\right)!}+\frac{10!}{6!\left(10-6\right)!}\\ \frac{10!}{2!\left(8\right)!}+\frac{10!}{6!\left(4\right)!}\\ \frac{10*9*8*7*6*5*4*3*2*1}{2*1\left(8*7*6*5*4*3*2*1\right)}+\frac{10*9*8*7*6*5*4*3*2*1}{6*5*4*3*2*1\left(4*3*2*1\right)}\\ \frac{10*9}{2*1}+\frac{10*9*8*7}{4*3*2*1}\\ 5*9+10*21\\ 45+210\\ 255\end{array}$