SOLUTION: There are 5 red, 5 blue, 5 green and 5 yellow letters, each of which is inside one of twenty identical unmarked envelopes. What is the least number of envelopes selected in order t

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Question 1088494: There are 5 red, 5 blue, 5 green and 5 yellow letters, each of which is inside one of twenty identical unmarked envelopes. What is the least number of envelopes selected in order to have at least 3 letters of the same color?
a.4 b.8 c.9 d.12
Answer by ikleyn(52785) About Me  (Show Source):
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Answer. c) 9.

Solution

In worst case you will select 2 red, 2 blue, 2 green and 2 yellow letters after 8 trials.

Then on the 9-th trial you INEVITABLY will get 3 letters of the same color, independently which exactly color you will select at this trial.