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There are two smaller problems in this one. First, is the fraction formed by the probabilities of the cards desired, then also there's the permutations of this fraction. Multiplying them together gives the total probability.

The permutations of the clubs and hearts in the hand are 4 + 3 + 2 + 1 = 10. Just for justification, there is (CCHHH), (CHCHH), (CHHCH), (CHHHC), (HCCHH), (HCHCH), (HCHHC), (HHCCH), (HHCHC), (HHHCC). So:

P(two clubs, three hearts) = 10 * (13 * 12 * 13 * 12 * 11) / (52 * 51 * 50 * 49 * 48) = 10 * (2432111132) / (29325272131171) = (11 * 13) / (16 * 5 * 49 * 17) = 143/66,640

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Q: How many five card hands chosen from a standard deck contain two clubs and three hearts?
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