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:

Three of a kind?

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

Number of ways of selecting 1 denominations out of 13 is C(13,1). Number of ways of selecting 3 cards out of 4 cards of selected denomination is C(4,3). And then select two denominations out of remaining 12 denominations is C(12,2) and then 1 card from each selected denominations is C(4,1)C(4,1). So number of ways are there to draw a 5 card poker hand that contains 3 a kind is

C(13,1)C(4,3)C(12,2)C(4,1)C(4,1) = 54912 ways

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.