I have a homework question to solve the number of ways to choose 25 ice creams of a selection of 6 types of ice creams and there are only 7 of each ice cream type.
The question requires the use of generating functions and I have gotten to this point: $({{x}^{48}}-6{{x}^{40}}+15{{x}^{32}}-20{{x}^{24}}+15{{x}^{16}}-6{{x}^{8}}+1)\cdot {{\left( \frac{1}{1-x} \right)}^{6}}$
But know I need to find the coefficient of $x^{25}$ and I don't know how to continue.
Can anyone please help?
Thanks a lot,