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Question
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Solution
Total number of king cards = 4
Ways to select one card from these = 4C1 = 4
Now ways to select 4 cards from the remaining 48 cards = 48C4 = `(48 xx 47 xx 46 xx 45)/(1 xx 2 xx 3 xx 4)`
= 194580
Thus the number of combinations by taking 5 cards out of 52 cards (1 of which is a king)
= 4C1 x 48C4 = 4 x 194580
= 778320
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