A seven card poker hand

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Question from Sean, a student:

I'm having trouble doing a probability problem concerning a seven card poker hand.

for the first part of the problem i think i did it right, but the second part is where i am struggling

a. from a standard card deck, seven cards are chosen at random.
find the probability that the set chosen contains exactly three of each of two different face values.
-----for this i answered (C(4,3)*C(4,3)*C(46,1)) / C(52,7)....is this right?

the second part of the problem asks the probability that the card hand contains exactly three 2's and exactly three 5's.
--i know that the answer to this is obviously a lower percentage than my first answer, are the answers related at all, any help provided would be really appreciated.

thanks,

Sean,

Actually, it's the first part where the problem is. But you're fairly close -I think-, so I'll make the hint not too detailed.

Try working out the corresponding two problems when the hand should have four cards of one type and three of the other. It should become obvious what's wrong - and what the number you've computed actually represents!

Good hunting!
RD

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