Question

What is the coefficient of the third term in the binomial expansion of (a + b)6? 1 15 20 90

Answer 1

15

Explanation:

Answer 2

Answer: 15

Explanation:

(r+1)th term of
`(a+b)^n` is given by:-

`T_(r+1)=\ ^nC_r(a)^(n-r)b^r`

For
`(a+b)^6` , n= 6

`T_3=T_(2+1)=\ ^6C_2(a)^(6-2)(b)^2\\\\`

`=\ (6!)/(4!2!)a^4b^2\ \ \ [^nC_r=(n!)/(r!(n-r)!)]\\\\=(6*5*4!)/(4!*2)a^4b^2\\\\=3*5a^4b^2\\\\ =15a^4b^2`

Hence, the coefficient of the third term in the binomial expansion of
`(a+b)^6` is 15.