Question

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?

Answer 1

1/311875200.

There is exactly 1 way to have all 5 of these cards.  For the first card, there are 52 total cards to be had; for the second, 51; for the third, 50; for the fourth, 49; and for the fifth, 48:

(1/52)(1/51)(1/50)(1/49)(1/48) = 1/311875200.