Sum of the coefficients of terms of degree 13 in the expansion of`(1+x)^(11) (1+y^(2)-z)^(10)` is

Options

A. A. `.^(10)C_(3)`
B. B. `.^(10)C_(4)`
C. C. `.^(11)C_(3)`
D. D. `.^(11)C_(4)`

Answer

B

Explanation

Required sum of coefficient
`=` coefficient of `t^(15)` in `(1+t)^(11) (1+t^(2) - t)^(100)`
`=` coefficeint of `t^(13)` in `(1+t)(1+t^(3))^(10)`
`=` coefficient of `t^(13)` in `((1+t^(3))^(10) + t(1+t^(3))^(10))`
`=` coefficient of `t^(12)` in `(1+t^(3))^(10)`
`= .^(10)C_(4)`