Question

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

10
15
21

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=(7!)/(2!(7-2)!)=(7!)/(2!5!)=(7* 6* 5!)/(2* 1* 5!)=7* 3=21.`

Thus, the required co-efficient is 21.

Option (C) is correct.