What is the probability that a 5 card poker hand contains the two of diamonds and the three of spades?

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What is the probability that a five-card poker hand contains the two of diamonds, the three of spades, the six of hearts, the ten of clubs, and the king of hearts?

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The total number of ways of a 5-card poker hand is: C( 52, 5 ).

The number of ways of the hand of cards which have to include 2 of diamonds and 3 of spades is:

C(1,1)C(1,1)C( 50, 3) = C( 50, 3 ). C(1,1) indicates that there only one way to get 2 of diamonds or 3 of spades. After we have these two in a hand there 50 cards left to hand the rest of the 5-card hand(3 cards left):C(50,3).

So the probability is: C(50, 3)/C(52, 5) = 0.00754