counting

Question

Find the number of ways of forming a committee of 9 people drawn from 3 different parties so that no party has absolute majority in committee?

Answer 1

4 ways : {1,4,4}, {4,1,4], {4,4,1}, {3,3,3}

Answer 2

From the given info,we can write as x1+x2+x3=9 and 1<=xi<=4( no party has absolute majority in committee)

Here the generating function would be (x+x^2+x^3+x^4)^3 (since x1,x2,x3 so cube)

so we need to find the coefficient of x^9 to get the answer

Comments

@ shah by above method  we will get those cases as well where one party will have majority right?by above method you will get  25 as answer  which is not equal to 4 right.