Two A-tiles, one B, one C

Question

A bag holds 5 tiles marked A, 4 tiles marked B, and 6 tiles marked C, 15 in total. You draw 4 tiles at random. What is the probability of drawing exactly 2 A-tiles, 1 B-tile, and 1 C-tile?

Accepted Answer

Choose the required number from each letter's pile, multiply, then divide by all ways to draw 4. Recall \binom{n}{k} counts ways to choose k from n. Total ways to draw 4 from 15: \binom{15}{4}=1365. Favorable ways: \binom{5}{2}	imes\binom{4}{1}	imes\binom{6}{1}=10	imes 4	imes 6=240. Divide: \frac{240}{1365}=\frac{16}{91}\approx 0.176. Takeaway. The recipe does not care how many colors there are: pick each type's quota from its pile, multiply, divide by the total ways to draw the handful.

Two A-tiles, one B, one C

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