Chapter 8, Problem 76RE

To determine

To find: Binomial coefficient using Pascal’s Triangle.

Answer to Problem 76RE

Binomial coefficient of $C{}_7$ is $36$ .

Explanation of Solution

Given information:

  $C{}_7$

Concept:

  $C{}_r$

Binomial coefficient of $C{}_r$ using Pascal triangle is given by

In ${\left(n+1\right)}^{th}$ row ${\left(r+1\right)}^{th}$ element is Binomial coefficient.

  $C{}_7$

Therefore,

Binomial coefficient is the number in ${\left(10\right)}^{th}$ row $8^{th}$ element.

Example of Pascal’s triangle is

  

Therefore,

Binomial coefficient of $C{}_7$ is $36$ .