Combination Formula: How many five-card poker hands

Fobian

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Sep 24, 2006
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4
Ok, here is the combination formula:

nCr= n!/(n-r)!r!

I know that I need to use this formula to figure this problem out, but I can't figure it out for the life of me!

How many five-card poker hands containing exactly 3 aces are possible?

Any suggestions?

Thanks
 
Choose 3 out of the 4 aces. C(4,3)

Then choose 2 out of the remaining non-ace cards. C(48,2)
 
Hint (1,2,3,4 = aces):
123
124
134
234

In each case, there's 48 cards left (not 49) to make up the last 2
 
That is why I use this formula: nCr= n!/(n-r)!r! right? Because order does not matter. If it did, I would use this forumula:

nPr = n!/(n-r)!

Correct?
 
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