5
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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$

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