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The coefficient of a^8b^4c^9d^9 in (a b ...

The coefficient of `a^8b^4c^9d^9` in `(a b c+a b d+a c d +b c d)^(10)` is

A

`10!`

B

`(10!)/(8!4!9!9!)`

C

`2520`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
`a^(10)b^(10)c^(10)d^(10)(1/a+1/b+1/c+1/d)^(10)`
Therefore the required coefficient is equal to the coefficient of
`a^(-2)b^(-6)c^(-1)d^(-1)` in `(1/a+1/b+1/c+1/d)^(10)`, which is given by
`= (10!)/(2!6!1!1!) = (10 xx 9 xx 8 xx 7)/(2) = 2520`
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