The coefficient of `x^(28)` in the expansion of `(1+x^3-x^6)^(30)` is `1` b. `0` c. `^30 C_6` d. `^30 C_3`

Options

A. 1
B. 0
C. `.^(30)C_(6)`
D. `.^(30)C_(3)`

Answer

B

Explanation

`(1+x^(3)-x^(6))^(30)`
`= {1+x^(3)(1-x^(3))}^(30)`
`=.^(30)C_(0) + .^(30)C_(1)x^(3)(1-x^(3))+.^(30)C_(2)x^(6)(1-x^(3))^(2) + "…."`
Obviously, each term will contain `x^(3m), m in N`. But 28 is not divisible by 3. Therefore ther will be no term containing `x^(28)`.