SOLUTION: A 5-card hand is dealt from a deck of 52 cards. What is the probability that exactly one card is a king?

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Probability is (total number of desired outcomes)/(total number of possibly outcomes)

Desired outcome: you want 1 king, and 4 other cards

To get that, you use combinatorics:
4C1 x 48C4 = 778320

Total outcome: 5 card hand

To get that, you do 52C5 = 2598960

Then the probability is
P(1 king in a 5 card hand)= 778320 / 2598960 = 0.299