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A box contains 5 red marbles, 8 green marbles, 11 blue marbles, and 15 yellow marbles. We draw marbles uniformly at random without replacement from the box. What is the minimum number of marbles to be drawn to ensure that out of the marbles drawn, at least 7 are of the same colour?

(A) 7

(B) 8

(C) 23

(D) 24

(E) 39
in Combinatory by (3.6k points) | 10 views

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In the worst case we’ll choose $5$ red marbles, $6$ green marbles, $6$ blue marbles and $6$ yellow marbles, before choosing the marble that’ll be the seventh marble of the same color (either green, blue or yellow).

So $5 + 6 + 6 + 6 + 1 = 24$ marbles.
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