What is the probability that all three are queens?

Question

Three cards are drawn in succession from a standard 52 card playing deck without replacement. What is the probability that all three are queens?

Answer 1

The order of the selection does not matter...

for example Queen of Hearts, Queen of Spades, Queen of Diamonds

is the same as:

Queen of Spades, Queen of Diamonds, Queen of Hearts

THe denominator is (52 choose 3) = 52*51*50/ (3*2*1) = 52*51*50/ 6 = 26*51*50/3 = 26*17*50 = 22100

the numerator is (4 choose 3) = 4/1 = 4

the probability is 4/22100 = 2/11050 = 1/5525 = 0.000181- = 0.0181- %