Chapter 8, Problem 59CR

To determine

To find: The find the binomial coefficient with the help of Pascal’s triangle.

Answer to Problem 59CR

The binomial coefficient is $21$ .

Explanation of Solution

Given:

The given expression is ${}_7{C}_7$ .

Calculation:

By sixth row of the Pascal’s triangle to determine the binomial coefficient as,

  $1615201561$

Then, the binomial coefficient ${}_7{C}_7$ is obtained by adding the second term, the sixth term and the 15^th term of the sixth row as,

  $\begin{array}{l}1615201561\\ 172135352171\\ {}_7{C}_0{}_7{C}_1{}_7{C}_2\end{array}$

Then,

  $\begin{array}{c}{}_7{C}_2=6+15\\ =21\end{array}$