Determine the number of 5 card combination out of deck of 52 cards if there is exactly one ace in each combination.
each of the four aces is combined with four of the other 48 cards
4 * 48C4
Ohhh thanks
To determine the number of 5-card combinations from a deck of 52 cards where there is exactly one ace in each combination, we can follow these steps:
Step 1: Calculate the number of ways to choose one ace. Since there are 4 aces in a deck, we have 4 possible choices.
Step 2: Calculate the number of ways to choose the remaining 4 cards from the remaining 51 cards in the deck. We can use the combination formula, which is given by:
C(n, r) = n! / (r!(n-r)!),
where C is the combination, n is the total number of items, and r is the number of items selected without regard to order.
In this case, we need to choose 4 cards from the remaining 51 cards. Using the combination formula, we get:
C(51, 4) = 51! / (4!(51-4)!) = 51! / (4!47!).
Step 3: Multiply the result from Step 1 by the result from Step 2 to obtain the total number of 5-card combinations with exactly one ace each.
Total combinations = 4 * (51! / (4!47!)).
After evaluating this expression, we get the final answer, which is the number of 5-card combinations with exactly one ace in a deck of 52 cards.