Find the probability of the following five-card poker hands from a 52-card deck. In poker, aces are either high or low. Two pair (2 cards of one value, 2 of another value)

Question

anonymous · Answer

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anonymous · Answer

22464 is incorrect :-/ completely lost

valpey · Answer

the number of ways to pick five cards out of 52 is 
$$\frac{52!}{47!*5!}$$
The number of ways to pick two pair is
13 possible first pairs with 6 suit combinations times
12 possible second pairs with 6 suit combinations
divided by two because 5588 is the same as 8855
times 11 possible extra cards times 4 possible suits.

valpey · Answer

so the numerator is
11*4*13*6*12*6/2
and the denominator is 
52*51*50*49*48/(5*4*3*2)

valpey · Answer

You can do a lot of cancellation before you get to the ultimate answer.

anonymous · Answer

5148

kropot72 · Answer

The answer should be a probability equivalent to approximately 4.75%

valpey · Answer

Try cancellation from here:
$$\frac{4*11*6*13*6*6}{52*51*5*49*4}$$

zarkon · Answer

are you trying to calculate the probability of 2-pair   ...2 cards of one rank and another 2 cards of the same but different rand from the first 2 and a 5th card of a rank different than the other 4?

anonymous · Answer

did you get an answer yet that you like?

anonymous · Answer

i can't say i like any of these choices hmmm

valpey · Answer

Yes, one of the answers is very close, but not correct. Maybe the deck is missing a card :)

anonymous · Answer

Thanks guys I got it and yes I was really close ;)