Chapter 8.4, Problem 74E

To determine

To evaluate:The binomial coefficient $C{}_2$ using Pascal’s triangle.

Answer to Problem 74E

  $C{}_2=10$

Explanation of Solution

Given:

A binomial coefficient as

  $C{}_2$

Using the Pascal’s triangle

  $\begin{array}{ccccccccccccccc}& & & & & & & 1& & & & & & & \\ & & & & & & 1& & 1& & & & & & \\ & & & & & 1& & 2& & 1& & & & & \\ & & & & 1& & 3& & 3& & 1& & & & \\ & & & 1& & 4& & 6& & 4& & 1& & & \\ & & 1& & 5& & 10& & 10& & 5& & 1& & \\ & 1& & 6& & 15& & 20& & 15& & 6& & 1& \\ 1& & 7& & 21& & 35& & 35& & 21& & 7& & 1\end{array}$

It is concluded that

  $C{}_2$ = 10,

The 3^rdentry in the 5^th row ,

Hence , $C{}_2$ = 10