In How Many Ways Can Three Aces Be Drawn From A Deck Of Cards?


3 Answers

Atul Chhotray Profile
Atul Chhotray answered
There are 4 Aces in a deck and hence 4 ways of drawing the first ace. Obviously the aces are not identical objects and the order in which they are arranged is important.

Now the pack contains 3 aces and so there are three ways of drawing the 2nd ace.

As a result of drawing two aces we have two aces left in our deck. So the third ace can be either one of them giving us a choice of two cards.

So number of ways = 4 * 3 * 2 = 24
yumi ishihara Profile
yumi ishihara answered
There are 3 different aces out of 4 in one deck of cards. From each card, you can get 1/13*4 possibilities of selecting.
Therefore,    3C4/4C52=3*4/4*52=12/208=3/52
52 cards exist in one deck of cards.

Three ways can be drawn.
thanked the writer.
Jonathan Naraine
Jonathan Naraine commented
I think ur using the combo rule. However if a person wants to know the same question when "order matters." you would have to use the permuation rule=n!/(n-r)!=24 possible ways
Oddman Profile
Oddman answered
There are 4*3*2 = 24 sequences in which 3 aces can be drawn from a deck containing 4 aces.
thanked the writer.
Jonathan Naraine
Jonathan Naraine commented
Question, i have the same problem, but i do not know how you came up with that answer. I am not following your equation.
Oddman commented
The first ace drawn can be of any of the four suits, clubs, diamonds, hearts, spades. The next ace drawn can be from any of the remaining 3 suits. The final ace will be from one of the remaining 2 suits. Thus 3 aces can be drawn in any of 24 sequences. The result of the draw will be one of 4 possible groups, distinguished by the one missing ace.

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