In how many ways can four aces be drawn from a deck of cards? (Order is not important.)
To find the number of ways four aces can be drawn from a deck of cards, you can use combinations.
The number of ways to choose four aces from a deck of cards (without considering order) is given by the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, we have n = 4 (the number of aces) and r = 4.
Plugging in the values into the combination formula, we get:
C(4, 4) = 4! / (4! * (4 - 4)!)
4! = 4 * 3 * 2 * 1 = 24
4! = 4 * 3 * 2 * 1 = 24
4 - 4 = 0
C(4, 4) = 24 / (24 * 0!)
Remember that 0! is defined as 1.
C(4, 4) = 24 / (24 * 1)
C(4, 4) = 24 / 24
C(4, 4) = 1
Therefore, there is only 1 way to draw four aces from a deck of cards (without considering order).
To find the number of ways four aces can be drawn from a deck of cards, we can use combinations.
Step 1: Determine the total number of aces in the deck. In a standard deck of 52 cards, there are 4 aces.
Step 2: Use the combination formula. The combination formula calculates the number of ways to choose a specific number of items from a larger set, where the order does not matter. The combination formula is given by:
C(n, r) = n! / (r! * (n-r)!)
where:
- n is the total number of items in the set
- r is the number of items we want to choose
In this case, we want to choose 4 aces from a set of 4 aces, so n = 4 and r = 4. Plugging these values into the combination formula:
C(4, 4) = 4! / (4! * (4-4)!)
= 4! / (4! * 0!)
= 4! / (4! * 1)
= 4! / 4!
= 1
Therefore, there is only 1 way to draw four aces from a deck of cards, where the order does not matter.