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The coefficient of a^{8}b^{4}c^{9}d^{9} in (abc + abd + acd +

Question

The coefficient of $a^{8} b^{4} c^{9} d^{9}$ in $(ab c + ab d + a c d + b c d)^{10}$ is

10!

\frac{10 !}{8 ! 4 ! 9 ! 9 !}

2520

None of these

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Lucas Discussed

The coefficient of

a^{8} b^{4} c^{9} d^{9}

(ab c + ab d + a c d + b c d)^{10}

12 mins ago

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12 mins ago

Text solutionVerified

(ab c + b c d + ab d + a c d)^{10}

can be written as

(ab c d)^{10} (a^{- 1} + b^{- 1} + c^{- 1} + d^{- 1})^{10}

Using binomial theorem, the coefficient of

a^{8} b^{4} c^{9} d^{9}

will be the coefficient of the powers

2, 6, 1, 1

, that is

= \frac{10 !}{2 ! 6 ! 1 ! 1 !} = 2520

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Question Text	The coefficient of $a^{8} b^{4} c^{9} d^{9}$ in $(ab c + ab d + a c d + b c d)^{10}$ is
Answer Type	Text solution:1
Upvotes	150