Discussion
A box has 6 black, 4 red, 2 white and 3 blue shirts. When 2 shirts are picked randomly, what is the probability that either both are white or both are blue?
Answer: A
The two cases cannot both happen, so add their counts.
\[ \text{both white} = {}^{2}C_{2} = 1, \qquad \text{both blue} = {}^{3}C_{2} = 3 \]
\[ P = \frac{1 + 3}{{}^{15}C_{2}} = \frac{4}{105} \]
With only two white shirts there is exactly one way to take both, which is what keeps the numerator so small.
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