Question 429255: In how many ways can three aces be drawn from a standard deck of 52 cards?
MY WORK SO FAR:
Im not sure which approach to take on this problem.
52 cards=n
3 aces=r
52!/(52-3)!
52!/49!
52x51x50x49x.../49x48x47x...
52x51x50=132,600
OR
I know there are 52 cards in a deck, 4 suits in a deck with one ace each, so 4 aces in a deck.
so...
n=4
r=3
4!/(4-3)!
4!/1!
4x3x2x1=24
I need help!
Found 2 solutions by sudhanshu_kmr, richard1234:
Answer by sudhanshu_kmr(1152)   (Show Source):
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! Your first "solution" actually suggested the number of ways to pick three of *any* card out of a deck of 52 cards, where the order does matter.
The second solution is closer, you picked three aces out of four cards, using the expression 4P3. However this over-counts quite a bit, because 4P3 assumes the order also matters. Since we are choosing three aces and the order is assumed not to matter, it would be represented as 4C3, or 4!/(3!1!), which is equal to 4.
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