Question

Which of the following would be the coefficient of the third term of a binomial to the seventh power?

Answer 1

Hello,

7C2=7*6/(2*1)=21

Other way: Pascal's triangle
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 <=================

Answer 2

Answer:  The correct option is (C) 21.

Step-by-step explanation:  We are given to select the correct option that would be the coefficient of the third term of a binomial to the seventh power.

We know that the co-efficient of r-th term in a binomial expression to the n-th power is given by

$^nC_{r-1}.$

In the given binomial expression,

n = 7  and  r = 3.

Therefore, the value of the co-efficient is

$^7C_{3-1}=^7C_2=\dfrac{7!}{2!(7-2)!}=\dfrac{7!}{2!5!}=\dfrac{7\times 6\times 5!}{2\times 1\times 5!}=7\times 3=21.$

Thus, the required co-efficient is 21.

Option (C) is correct.