IIT JEE , AIEEE Forum - Mathematics , Algebra

KAB

Its based on multinomial theorem which is as follows,

(a₁+a₂+.....+a_m)ⁿ= {n!(a₁ⁿ¹)(a₂ⁿ²).......(a_m^nm)}/(n₁!n₂!......n_m!)

Where n₁+n₂+n₃+....+n_m=n

In this problem,

a₁=1 a₂=x a₃=y a₄= -z n=9

So

(1+x+y-z)⁹=

{9!(1^ax^by^c(-z)^d)}/(a!b!c!d!)

Where a+b+c+d=9

Here since co-efficient of x³y⁴z is required a=1 b=3 c=4 d=1

So the co-efficient of x³y⁴z is -9!/1!3!4!= -2*9C2*7C3