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​

Answer 1

Answer:

Sol: Given that 5 card combination should have at least one king card and 4 non king card . We know that a pack of 52 cards contains 4 king cards and 48 non king cards. One king card from 4 king cards can be selected 4c1 ways, also 4 non king cards from 48 non king cards can be selected in 48c4 ways. Required number of 5 card combination = 4c1x48c4 = 778320. Two king cards from 4 king cards can be selected 4c2 ways, also 3 non king cards from 48 non king cards can be selected in 48c3 ways. Required number of 5 card combination = 4c2x48c3 = 103776 Three king cards from 4 king cards can be selected 4c3 ways, also 2 non king cards from 48 non king cards can be selected in 48c2 ways. Required number of 5 card combination = 4c3x48c2 = 4512 Four king cards from 4 king cards can be selected 4c4 ways, also 1 non king cards from 48 non king cards can be selected in 48c1 ways. Required number of 5 card combination = 4c4x48c1 = 48 Total number of required combination = 778320 + 103776+ 4512+48 = 886656 ways.

Step-by-step explanation:

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