rakeshd347 wrote:If a box contains 10 red pills, 5 blue pills, and 12 yellow pills, what is the least number of pills one must extract from the box to ensure that at least three pills of each color are among those extracted?
12
17
18
23
25
OA is E
As noted above, this is a WORST-CASE SCENARIO problem.
To GUARANTEE that 3 of each color are chosen, we must determine the worst-case scenario: the greatest number of marbles that can be removed WITHOUT choosing at least 3 of each color.
If all of the yellow pills and all of the red pills are removed first, the number of pills removed = 12+10 = 22.
Since there are more yellow pills and red pills than blue pills, 22 is the maximum number of pills that can be removed without choosing at least 3 of each color.
To remove at least 3 of each color, 3 blue pills must now be chosen, yielding the following total:
22+3 = 25.
The correct answer is
E.
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