Probability Q

[DentalKitty]

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I just made this problem up so please tell me if it doesn't make sense.

If you have a deck of cards, how many ways can you have 3 jacks in a hand of 5 cards?

*edit* I mean different hands of 5 cards that contain 3 jacks

Would it be 49*48*3*2*1? Or 4*3*2*49*48? Something else? I'm just trying to think of things they could ask, thanks!

 

[Streetwolf]

I just made this problem up so please tell me if it doesn't make sense.

If you have a deck of cards, how many ways can you have 3 jacks in a hand of 5 cards?

*edit* I mean different hands of 5 cards that contain 3 jacks

Would it be 49*48*3*2*1? Or 4*3*2*49*48? Something else? I'm just trying to think of things they could ask, thanks!

(4 choose 3) --> chooses the 3 suits of the Jacks in your hand
(48 choose 2) --> chooses the last 2 cards in your hand. Use 48 because you have accounted for 3 Jacks, and you don't want a 4th Jack. This leaves 48 cards in the deck to choose from.

4 choose 3 = 4
48 choose 2 = 1,128

4x1128 = 4,512

Of course this includes both 3 of a kind and full house hands.

 

[DentalKitty]

Oh I see now. You have to treat each piece separately and then multiply. Thanks a lot!