How many ways to get a Four of a kind?

[gillgill]

Poker hands...

1. How many ways are there to obtain these three highly-rated combinations below?
a. Four of a kind. -Four cards of the same rank and one other card

b. Full House. -Three cards of the same rank and two cards both of another rank. ( A triple, or three of a kind, and a pair.)

c. Two pairs. -Two pairs of cards of two distinct ranks and a fifth card of another rank.

2. Suppose you play a game in which only three cards are deal: How many ways are there to obtain one pair?

3. Suppose four cards are dealt. How many ways are there to obtain one pair?

am i doing these correctly?
1a. 13C1 X 48C1 = 624
b.13C1 X 4C3 X 12C1 X 4C2 = 3744
c.13C2 X 4C2 4C2 44C1 = 123,552

2.13C1 X 4C2 X 12C1 X 4C1 = 3744

3. 13C1 X 4C2 X 12C1 X 4C1 X 11C1 X 4C1 = 164736

am i right?

 

[TenaliRaman]

Hmm, a flash review of your answers suggests to me you are correct

-- AI

 

[cepheid]

You seem to know what you're doing gillgill. So why the doubt?

 

[gillgill]

thanks...