# Discrete Mathematics - Ice Cream random samples

How would you solve the following problem with Discrete Mathematics, and what is the answer?

Suppose there are 5 different types of ice cream you like. How many random samples ice cream must be eaten to guarantee that you have had at least 7 samples of one type?

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Please share with us your thoughts on the problem. –  Sasha Dec 6 '12 at 17:29
I don't have any, discrete is impossible –  NoDiscrete Dec 6 '12 at 17:32
Hint : You can think of this as a generalization of the pigeon hole principle. –  Siméon Dec 6 '12 at 17:39

HINT: You can eat $30$ samples without getting $7$ of the same type; how? What happens if you eat more than that?
Hint: If you have eaten $(5)(6)$ samples, you might not have eaten $7$ of any flavour, since you might have eaten $6$ of each dlavour. But anything over that $\dots$. In your answer, you might be expected to mention and use the Pigeonhole Principle.