In how many ways can four pictures be selected from a group of nine different pictures?
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To find out in how many ways four pictures can be selected from a group of nine different pictures, we need to apply the concept of combinations.
The number of ways to select four pictures from a group of nine can be calculated using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)
Where:
- C(n, r) represents the number of combinations of n items taken r at a time.
- n! represents the factorial of n, which is the product of all positive integers from 1 to n.
- r! represents the factorial of r.
- (n-r)! represents the factorial of (n - r).
In this case, we want to calculate C(9, 4), which is:
C(9, 4) = 9! / (4! * (9-4)!)
Let's break down the calculation step by step:
1. Calculate the factorial of 9: 9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 362,880
2. Calculate the factorial of 4: 4! = 4 * 3 * 2 * 1 = 24
3. Calculate the factorial of (9 - 4): (9 - 4)! = 5! = 5 * 4 * 3 * 2 * 1 = 120
4. Substitute the calculated values into the combination formula:
C(9, 4) = 362,880 / (24 * 120) = 362,880 / 2,880 = 126
Therefore, there are 126 ways to select four pictures from a group of nine different pictures.
Really?
That's a post per minute. How about telling us where your troubles
are with these questions. You show no work or effort on your part.
You weren't possibly expecting us to just do your work for you?