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
[tex]^nC_{r-1}.[/tex]
In the given binomial expression,
n = 7 and r = 3.
Therefore, the value of the co-efficient is
[tex]^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.[/tex]
Thus, the required co-efficient is 21.
Option (C) is correct.
