Grandma has 8 grandchildren, and 4 different types of popsicles:
- 6 Vanilla popsicles
- 6 Strawberry popsicles
- 5 Banana popsicles
- 3 Chokolate popsicles
This morning, all of her grandchildren came together and asked for one popsicle each (every grandchild asked for a particular flavor). What is the total number of different sets of requests that Grandma can fulfill?
I think this is related to the Inclusion-Exclusion principle because it was taught in the same class. Can you help me solve it?
I did reach the following sum, but I imagine the question's author had something simpler in mind...
$ E(0) = W(0)-W(1) = 3^8 - 4\cdot C(8,8)-4\cdot 3\cdot C(7, 8)-2\cdot C(6, 8)\cdot 3^2-C(5, 8)\cdot 3^3 - C(4, 8)\cdot 3^4$