# two cards are drawn at once,from pack of 52. Find the chance of drawing two aces?

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There are 4 aces amongst the 52 cards, so the number of ways to draw 2 aces is the binomial coefficient C(4,2) = 4! / (2!·2!) = (4·3) / 2! = 6.

The total number of ways to draw 2 cards from the deck of 52 is, likewise, C(52,2) = 52·51 / 2! = 26 x 51.

So the required probability is

C(4,2) / C(52,2) = 6 / (26·51) = 1 / (13·17) = 1/221 = 0.00452...

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• 1:221

4/52 is your odds of drawing one ace from the full deck

3/51 is your odds of drawing an ace from the rest of the deck - this is true even though you are drawing at the same time because you cannot draw the same card twice, and since the first must be an ace

the number of aces reduces by one as well as the number of cards drawn from.

4/52*3/51 gives us the combined odds of 12/2652 or 1/221.

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• The answer is P(tow aces from 1 draw) = 13/52 X 12/52

Pease Calculate

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• Total number of ways to draw any two cards: 52!/(52-2)! = 52x51

Total number of ways to arrange the two aces: 4!/(4-2)! = 4x3

Divide the total number of ways to arrange the aces by the number of ways to draw any two cards:

(4x3)/(52x51)

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