Question 1165005: In a deck of cards, what is the probability of drawing five black cards without repetition? With solution Found 2 solutions by solver91311, Edwin McCravy:Answer by solver91311(24713) (Show Source):
What do you mean by "without repetition"? Do you mean without replacement? Or do you mean that you are replacing the cards, but drawing the exact same card twice or more is a failure of the experiment?
John
My calculator said it, I believe it, that settles it
Are you talking about putting them back after you draw them or not? That
makes a difference in the answer.
If you're putting them back each time and must not draw the same card twice,
then
The probability that the first card is black is 13/52.
The probability that the second card is a different black card is 12/52.
The probability that the third card is a different black card is 11/52.
The probability that the fourth card is a different black card is 10/52.
The probability that the fifth card is a different black card is 9/52.
(13/52)(12/52)(11/52)(10/52)(9/52) = 1485/3655808
If you're NOT putting them back each time and thus cannot possibly draw the
same card twice, then
The probability that the first card is black is 13/52.
The probability that the second card is a different black card is 12/51.
The probability that the third card is a different black card is 11/50.
The probability that the fourth card is a different black card is 10/49.
The probability that the fifth card is a different black card is 9/48.
(13/52)(12/51)(11/50)(10/49)(9/48) = 33/66640
Edwin
