document.write( "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? \n" ); document.write( "

Algebra.Com's Answer #756257 by greenestamps(13209) $\"\"$ $\"About$

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\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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.

\n" ); document.write( "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).

\n" ); document.write( "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.

\n" ); document.write( "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. \n" ); document.write( "

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