A list of poker hands ranked in order from the highest to the lowest is shown in

Question

A list of poker hands ranked in order from the highest to the lowest is shown in the following table, along with a description and example of each hand. Use the table to answer the question.

If a 5-card poker hand is dealt from a well-shuffled deck of 52 cards, how many different hands consist of the following:

Four of a kind?

? different hands

Hand      Description      Example Straight
flush 5 cards in sequence
in the same suit A   2   3   4   5 Four of
a kind 4 cards of the same
rank and any other
card K   K   K   K   2 Full
house 3 of a kind and a
pair 3   3   3   7   7 Flush 5 cards of the same
suit that are not
all in sequence 5   6   9   J   K Straight 5 cards in sequence
but not all of the
same suit 10   J   Q   K   A Three
of a
kind 3 cards of the
same rank and 2
unmatched cards K   K   K    2   4 Two
pair 2 cards of the same
rank and 2 cards
of any other rank
with an unmatched
card K   K   2   2   4 One
pair 2 cards of the
same rank and 3
unmatched cards K   K   5   2    4

Explanation / Answer

Solution :

Choose 1 of 13 denominations to get four cards and combine with 1 card from the remaining 48. So the answer is (13C1)(48C1) = 624

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