Question

Suppose you choose 5 cards from a standard 52-card deck (with 13 hearts, 13 spades, 13 clubs and 13 diamonds). How many different choices of cards are possible if a. you can choose any 5 cards from the deck? b. all 5 cards must be hearts? c. you must choose four kings and one queen? d. you must choose 3 kings and no queens? e. you must choose at least 1 king and at least 2 aces?

Answer #1

(b) no. of ways = =
1287.

(c) no. of ways =
= 4.

(d) no. of ways =
= 3784, since first 3 cards must be 3 out of 4 kings and remaining
2 cards must be selected after excluding 4 kings and 4 queens from
the deck of cards.

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