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Find the number of ways of obtaining one club when drawing a 7 card hand from an ordinary deck

combination or permutation?

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2 Answers

There are 13 clubs and 39 cards of other suits.

If you want exactly one club:

C(13,1)*C(39,6) = 42414099

If you want at least one club:

C(52,7) - # of hands with no clubs = C(52,7) - C(39,7) = 130521937

It's a combinations question because the order of the cards does not matter - getting the club first or second or third etc is not important. Changing the order of the cards of a 7-card poker hand does not change the value of the hand - eg 2 7 A K A Q Q is the same no matter what order you put the cards in. Roman already provided how to find the answer.