What is the minimum of shirts that must be selected to ensure five shirts of the same color are selected?-Pigeonhole Principle

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A closet has 3 red, 7 blue and 10 black shirts. What is the minimum number of shirts you’ve to blindfoldedly pick to ensure a. at least 4 of the same color? b. at least 5 of the same color?

Soln: I tried working on it like this: 3 containers for the 3 colors. So ceil(N/3)=4 for the first one. Then N should be 10.

Similarly for the second one, ceil(N/3)=5, so N should be 13.

But I think my answer is wrong because there are only 3 red shirts, we can't pick 4 of the same color taking that into consideration. I do not have the answers. Please explain. Thank you :)

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Your answer to the first question is correct.

For the second one, think of the worst case scenario, namely that you first select $3$ red shirts, $4$ blue shirts, and $4$ black shirts. That means you can pick $11$ shirts without picking $5$ of the same color. However, if we pick $12$ shirts, we must have either $5$ blue shirts or $5$ black ones.