SOLUTION: 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?

Question 1109615: 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?
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

Choose the common rank of the three in 13C1 ways.
Choose the suits for the three in 4C3 ways
Choose the two different ranks of the other two cards in 12C2 ways,
to prevent the hand from being either four of a kind or a full
house.
Choose the suit for the higher ranking other card in 4C1 ways.
Choose the suit for the lower ranking other card in 4C1 ways.

Answer: (13C1)(4C3)(12C2)(4C1)(4C1) = 54912 ways.

Edwin

RELATED QUESTIONS
if a 5 card poker hand is dealt with a well-shuffled deck of 52 cards what is the... (answered by math_helper)

A hand consists of 5 cards from a well-shuffled deck of 52 cards. a. Find the total... (answered by Boreal)

A hand consists of 5 cards from a well-shuffled deck of 52 cards. a. Find the total... (answered by Boreal,Alan3354)

A hand consists of 3 cards from a well shuffled deck of 52 cards. a.Find the number of... (answered by Edwin McCravy)

What is the probability of being dealt a four card hand from a well shuffled deck of 52... (answered by lynnlo,stanbon)

A poker hand consists of five cards dealt from a deck of 52. How many diferent poker... (answered by checkley71)

A hand consists of 4 cards from a well-shuffled deck of 52 cards. a. Find the... (answered by jorel1380)

How many different 5-card hands can be dealt from a standard deck of 52... (answered by funmath)

how many different 5-card hands can be dealt from a standard deck of 52... (answered by ewatrrr)