sud21 wrote:Before leaving for his business trip, Chad asks his assistant to choose and pack four shirts from his closet, which currently contains eight shirts. If each shirt is a different color, including one blue shirt and one pink shirt, and the assistant chooses the shirts at random, what is the probability that the pink shirt will be one of the four packed but the blue shirt will not?
4/7
1/2
27/70
2/7
9/35
P = (good combinations)/(all possible combinations).
All possible combinations:
From 8 shirts, the number of ways to choose 4 = 8C4 = (8*7*6*5)/(4*3*2*1) = 70.
Good combinations:
In a good combination, 3 non-blue shirts are packed with the pink shirt.
From the 6 non-pink and non-blue shirts, the number of ways to choose 3 to be packed with the pink shirt = 6C3 = (6*5*4)/(3*2*1) = 20.
Thus:
(good combinations)/(all possible combinations) = 20/70 = 2/7.
The correct answer is
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