A box contains 12 black and 8 green marbles. How many ways can 3 black and 2 green marbles be chosen?
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The simplest solution is to calculate the probability none of the 3 is red, then subtracting that number from 1 gives the answer.
The number of possible triplets = 20!/(17! 3!)=20*19*18/6=1140
The number of non red cases = 8!/(5! 3!) = 8*7*6/6=56
The probability at least 1 is red = 1 -56/1140 =.9508
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