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Q.

The coefficient of a8b4c9d9 in (abc+abd+acd+bcd)10 is

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a

10!

b

10!8!4!9!9!

c

2520

d

5040

answer is C.

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Detailed Solution

a10b10c10d101a+1b+1c+1d10General term=10!p1!p2!p3!p4!1ap11bp21cp31dp4     where p1+p2+p3+p4=10Therefore the required coefficient is equal to the coefficient ofa−2b−6c−1d−1 in 1a+1b+1c+1d10, which is given by10!2!6!1!1!=10×9×8×72=2520
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The coefficient of a8b4c9d9 in (abc+abd+acd+bcd)10 is