SOLUTION: Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a club, and the third card is a 2?

Question 1189404: Three cards are dealt at random from a standard deck of 52 cards. What is the probability that the first card is a 4, the second card is a club, and the third card is a 2?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The possibilities are
4C*Club not 2*2
4C*2C*2
look at these. The first has probability of 1/52*12/51*4/50=48/132600
The second is 1/52*1/51*3/50=3/132600
4D,4H,4S* club not 2*2
same*2C*2
The first is (3/52)(12/13)(4/50)=144/132600
The second is (3/52)*1/51*(3/50)=9/132600
the sum is 204/132600=1/650
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rough check using sampling with replacement and ignoring double counting (1/13)(1/4)(1/13)=1/676
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