One of each color in three draws

Question

A bag holds 6 red marbles, 3 white marbles, and 3 blue marbles, 12 in total. You draw 3 marbles at random. What is the probability of drawing exactly one of each color: one red, one white, one blue?

Accepted Answer

Choose one from each color's pile, multiply, then divide by all ways to draw 3. Here \binom{n}{k} counts ways to choose k from n. Total ways to draw 3 from 12: \binom{12}{3}=220. Favorable ways: \binom{6}{1}	imes\binom{3}{1}	imes\binom{3}{1}=6	imes 3	imes 3=54. Divide: \frac{54}{220}=\frac{27}{110}\approx 0.245. Takeaway. "One of each" is the friendliest multivariate case: just multiply the three color counts and divide by the total ways to draw. No exponents or repeated combinations needed.

One of each color in three draws

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