You are given a standard deck of 52 playing cards. You draw five cards at random without replacement. What is the probability that you have drawn exactly one king?
Let's break down this problem step-by-step:

1. There are 4 kings in a standard deck of 52 cards.
2. To calculate the probability, we need to find the number of ways to draw exactly one king and divide it by the total number of possible card combinations when drawing five cards.
3. The number of ways to choose one king from four available kings is C(4,1) = 4 (combinations formula).
4. After choosing one king, there are 48 remaining non-king cards in the deck. We need to choose four more cards from these 48.
5. The number of ways to choose four cards from 48 is C(48,4) = 194580.
6. So, the number of ways to draw exactly one king is 4 * 194580 = 778320.
7. The total number of possible card combinations when drawing five cards from a deck of 52 is C(52,5) = 2598960.
8. Therefore, the probability of drawing exactly one king is 778320 / 2598960 ≈ 0.299.

The final answer is that the probability of drawing exactly one king is approximately 0.299 or 29.9%.