Recall that a standard 52-card deck has four suits, ♥, ♦, ♣, and ♠, each of...

Recall that a standard 52-card deck has four suits, ♥, ♦, ♣, and ♠, each of which has13cards, one each of the following kinds, A, K, Q, J,10,9,8,7,6,5,4,3,and2. A hand of seven (7) cards is drawn at random from such a deck. (This means that you get the cards as a group, in no particular order, and with no possible way of getting the same card twice in the hand.) Find the probability that the hand . . .

1. 2. 3.

4. 5.

... is a flush, i.e. all the cards in the hand are from the same suit. [1]

. . . has four cards of the same kind. [1]

. . . has exactly three cards of one kind, two cards of another kind, and two cards of yet another kind. [1]

. . . has cards of seven different kinds. [1]

... is a straight, i.e. a set of cards that can be arranged to be consecutive with no gaps in the sequence AKQJ1098765432, where we allow the sequence to wrap around the end. (So 3 2 A K Q J 10 would count as a straight, for example.) [1]

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Colby Messinger answered 2 years ago

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