Discrete Mathematics - Ice Cream random samples

Question

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?

Hint : You can think of this as a generalization of the pigeon hole principle. — Siméon, Dec 06 '12 at 17:39

score 1 · Answer 1 · answered Dec 06 '12 at 17:32

1

HINT: You can eat $30$ samples without getting $7$ of the same type; how? What happens if you eat more than that?

answered Dec 06 '12 at 17:32

Brian M. Scott

631,399

score 1 · Answer 2 · edited May 27 '19 at 09:30

1

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 flavour. But anything over that $\dots$. In your answer, you might be expected to mention and use the Pigeonhole Principle.

edited May 27 '19 at 09:30

N. F. Taussig

79,074

answered Dec 06 '12 at 17:35

André Nicolas

514,336

Discrete Mathematics - Ice Cream random samples

2 Answers2

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