Question 529602: If two cards are drawn from a standard 52 card deck without replacement, in how many different ways is it possible to obtain a heart on the first draw and an ace on the second?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If two cards are drawn from a standard 52 card deck without replacement, in how many different ways is it possible to obtain a heart on the first draw and an ace on the second?
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# of ways to succeed: 12*4 ways to pick a heart, not the ace of hearts,
followed by an ace = 48
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# of ways to succeed; 1 way to pick ace of hearts followed by ace = 1*3 = 3
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Total ways to succeed: 51
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Total # of random pairs: 52C2 = 1326
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Probability = 51/1326 = 0.0385
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Cheers,
Stan H.
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Answer by josmiceli(19441)  (Show Source):
You can put this solution on YOUR website! I'd get a 2nd opinion on this, but here's my view:
There are 13 ways that you can draw a heart first
Having drawn the heart, there are 4 ways to draw
an ace, so there are  ways to get
this combination. But what if the 1st card is the
Ace of hearts. Then there are only 3 ways to draw
an Ace. So I have to subtract the one combination
that I counted twice, that is Ace of hearts and
Ace of hearts again.
There are then 51 ways to draw a heart and then
an Ace. Hope I got it.
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