The question was : Determine the number of 5 card combinations cut of a deck of 52 cards if there is exactly one ace in each combination

To solve this problem, we need to use the concept of combinations in probability.

Step 1: Determine the number of ways to choose 1 Ace from the 4 available. This is a combination problem where we are choosing 1 item (Ace) from a larger set (4 Aces). The formula for combinations is C(n, k) = n! / [k!(n-k)!], where n is the number of items to choose from, k is the number of items to choose, and "!" denotes factorial. So, C(4, 1) = 4! / [1!(4-1)!] = 4.

Step 2: Determine the number of ways to choose the remaining 4 cards from the 48 non-Ace cards (since there are 52 cards in a deck and 4 are Aces). This is also a combination problem, so we use the same formula: C(48, 4) = 48! / [4!(48-4)!] = 194580.

Step 3: Multiply the results from Step 1 and Step 2 to get the total number of 5-card combinations with exactly one Ace. So, 4 * 194580 = 778320.

So, there are 778320 different 5-card combinations that can be drawn from a 52-card deck where exactly one of the cards is an Ace.