Probability of 3 Hearts in Same Hand: Combinatorics Question for Standard Bridge

[mehrts]

You're playing standard bridge with three other people. If you know that you and your partner have 10 hearts altogether, then what is the probability that the remaining 3 hearts are all in the same hand ?

Is it comb(3,3)*comb(23,10)/comb(26,13) ? Since there is only 1 way of selecting 3 hearts and com(23,10) ways of selecting the other 10 cards and comb(26,13) different combinations for the opponents cards ?

 

[0rthodontist]

So in bridge, is every card in somebody's hand? And each person always has 13 cards?

What you've said is the probability that the remaining three hearts in a particular person's hand. But there are two possible hands it could be in. What you're looking for is:
1. The number of ways for person A to select 3 hearts and 10 other cards (you basically have this already)
2. The number of ways for person A not to select 3 hearts, and then for person B to select the remaining cards.
Add up 1 and 2 and divide by the total number of ways for A and B to select their cards.

 

[mehrts]

Thanks that is what I thought. he he he :)