Could this be calculated using the complement of the event? And if so, how?
2026-03-25 08:13:45.1774426425
What is the probability of a poker hand (5 cards) containing at least one club?
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Yes, and using the complement is probably the simplest way. The complement of a hand having at least one club is a hand having no clubs, so the desired probability is
$$1 - \frac{\binom{39}{5}}{\binom{52}{5}}.$$