SOLUTION: If you draw 4 cards from a standard deck (52 cards), what is the probability that you get a two, a four, a six, and an eight (in any order)?

Question 275515: If you draw 4 cards from a standard deck (52 cards), what is the probability that you get a two, a four, a six, and an eight (in any order)?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
there are 4 twos in the deck.
there are 4 fours in the deck.
there are 4 sixes in the deck.
there are 4 eights in the deck.

the probability that you will draw a two and then a four and then a six and then an eight would be 4/52 * 4/51 * 4/50 * 4/49 = (4*4*4*4)/(52*51*50*49) = .0000394.

this can happen in 4*3*2*1 ways = 24 ways.

the probability is 24 * .0000394 = .000945609

here's how it would look.

each draw can happen in a certain order:

that order is shown below;

example:

2468 means a 2 is drawn first, then a 4, then a 6, then an 8.

here's a list of the possible order of draws.

2468
2486
2648
2684
2846
2864

4268
4286
4628
4682
4826
4862

6248
6284
6428
6482
6824
6842

8246
8264
8426
8462
8624
8642

each one of these draws is totally independent of the other.

the probability for any one of these draws is the same.

that probability = (4*4*4*4)/(52*51*50*49)

total probability is 24 * (4*4*4*4)/(52*51*50*49) = 24 * .0000394 = .000945609

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