SOLUTION: a bag contains 18 small red,19 small black,13 large black, and 15 large red t-shirt and nothing else.what is the least number of t-shirt alpa must take out from the to make sure sh

Question 1138440: a bag contains 18 small red,19 small black,13 large black, and 15 large red t-shirt and nothing else.what is the least number of t-shirt alpa must take out from the to make sure she has at least one of each color and size?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52878) (Show Source): You can put this solution on YOUR website!
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It depends, if the person who makes the choice, sees what he (or she) is doing.

Answer by greenestamps(13209) (Show Source): You can put this solution on YOUR website!

The response by tutor @ikleyn is appropriate; for this to be a properly presented problem, it must be stated that the t-shirts are taken out one at a time without looking -- i.e., randomly.

In that case, to determine the minimum number of t-shirts that must be taken out to get one of each color and size, consider the worst case scenario.

The worst case is if you pick all of the socks of 3 of the 4 kinds before you pick the first one of the last kind.

And to make the worst case the worst it can be, the kind of t-shirt you pick last needs to be the one of which there are the fewest (so that the number of t-shirts picked before is as large as possible).

So the worst case is where you pick all 52 of the small red, small black, and large red t-shirts before picking the first of the 13 large black t-shirts.

So the number of t-shirts that must be picked to make sure she has at least one of each kind is 52+1 = 53.
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