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Question

Let the coeffcient of x4 in the expansion of(1+x+x2+x3)11 be K. Find sum of digits of K.

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Solution

x4 can be achieved in following ways
(x)4(x2)0(x3)017 or (x)2(x2)1(x3)018 or (x)1(x2)0(x3)119 or (x)0(x2)2(x3)019
Hence the required coefficient will be
=11!4!.7!+11!1!.2!.8!+11!1!.1!9!+11!2!.9!
=330+495+110+55
=550+330+110
=990

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