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