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Question

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

A
10!
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B
1260
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C
5040
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D
2520
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Solution

The correct option is D 2520
(abc+abd+acd+bcd)10=a10b10c10d10(1a+1b+1c+1d)10=a10b10c10d10(a1+b1+c1+d1)10

The coefficient of a8b4c9d9 is equal to the coefficient of a2b6c1d1 in
(a1+b1+c1+d1)10

=10!2!6!1!1!=10!2!6!=10×9×8×72=2520

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