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 atrandom from such a deck. (This means that you get the cards as agroup, in no particular order, and with no possible way of gettingthe same card twice in the hand.) Find the probability that thehand . . .
1. 2. 3.
4. 5.
... is a flush, i.e. all the cards in the hand are from the samesuit. [1]
. . . has four cards of the same kind. [1]
. . . has exactly three cards of one kind, two cards of anotherkind, 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 tobe consecutive with no gaps in the sequence AKQJ1098765432, wherewe allow the sequence to wrap around the end. (So 3 2 A K Q J 10would count as a straight, for example.) [1]
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