A person is dealt five cards from an ordinary pack of 52 playing cards. What is theprobability that among the five cards there will be at least one king?

To solve this problem, it's easier to calculate the probability of not getting a king in 5 cards and then subtract that from 1.

Step 1: Calculate the total number of ways to draw 5 cards from a deck of 52. This is a combination problem, so we use the combination formula C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and "!" denotes factorial. So, C(52, 5) = 52! / [5!(52-5)!] = 2,598,960.

Step 2: Calculate the total number of ways to draw 5 cards from a deck of 48 (since we're excluding the 4 kings). So, C(48, 5) = 48! / [5!(48-5)!] = 1,712,304.

Step 3: The probability of not drawing a king in 5 cards is the number of ways to draw 5 cards without a king divided by the total number of ways to draw 5 cards. So, 1,712,304 / 2,598,960 = 0.6588.

Step 4: The probability of drawing at least one king in 5 cards is 1 minus the probability of not drawing a king. So, 1 - 0.6588 = 0.3412 or 34.12%.