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6 cards are drawn at random from a standard deck without replacement. Find the probability that all cards are hearts?

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6 cards are drawn at random from a standard deck without replacement. Find the probability that all cards are hearts?
posted Aug 8, 2017 by anonymous

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1 Answer

+1 vote

0.0084%
.
For the 1st card the chance for heart is 13/52
For the 2nd card the chance for that card to also be heart is 13/52 * 12/51 (12 heart remaining in a deck with 51 cards remaining).
For the 3rd card the chance for that card to be heart as well is 13/52 * 12/51 * 11/50
etc.
So for the 6th card the chance that all 6 cards are heart is 13/52 * 12/51 * 11/50 * 10/49 * 9/48 * 8/47 = 0.000084 or 0.0084%

answer Aug 8, 2017 by Jcm
We can have same by 13C6/52C6 I.e choosing 6 out of 13/choosing 6 out of 52
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