Pigeonhole principle practice problem 1

Probability Level 1

A Professor tells 3 Jokes in his ethics class each year.How large a set of jokes does the professor need in order never to repeat the exact same triple of jokes over a period of 12 years?

The answer is 6.

1 solution

Brian Charlesworth
Apr 20, 2015

We need to find the least positive integer $n$ such that $\dbinom{n}{3} \ge 12.$

Now $f(n) = \dbinom{n}{3}$ is an increasing function for integers $k \ge 3.$ So since $f(5) = 10$ and $f(6) = 20$ we can conclude that the professor needs at least $\boxed{6}$ jokes to choose from.

The problem I have with this question is the use of the word "triple". Usually triple is taken to mean that it is a permutation which gives 4 3 2>12, so the answer would be 4. A better wording would be "so that he doesn't tell the same set of 3 jokes in 12 years"

Brennan Ravan - 3 years ago

yeah it should have been so that he doesn't tell the same set of 3 jokes in 12 years

shlok panch - 2 weeks ago

Pigeonhole principle practice problem 1

The answer is 6.

1 solution

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