Question

What is the probability of getting all diamonds if 10 cards are selected without replacement

Answer 1

There are 52 cards total


There are 13 diamond cards.


So on the first pick, the probability is 13/52


There are now 13 - 1 = 12 diamond cards out of a total of 52 - 1 = 51 cards


So on the second pick, the probability is 12/51


There are now 12 - 1 = 11 diamond cards out of a total of 51 - 1 = 50 cards


So on the third pick, the probability is 11/50


....etc...


this pattern keeps going...


on the last pick (10th pick), there are only 4 diamonds left out of 43 cards total left over


So the last probability is 4/43


Now multiply all the probabilities together to get


(13/52)(12/51)(11/50)(10/49)(9/48)(8/47)(7/46)(6/45)(5/44)(4/43)


1037836800/57407703889536000


1/55314770



So the probability is 1/55314770