Find the number of combinations (subsets) of 9 things taken 5 at a time.
The number of combinations of n things taken k at a time is denoted by C(n, k) and is calculated using the formula:
C(n, k) = n! / [k! * (n - k)!]
where n! denotes the factorial of n, which is the product of all positive integers from 1 to n, and k! is the factorial of k.
For your case, n = 9 and k = 5, so we calculate it as follows:
C(9, 5) = 9! / (5! * (9 - 5)!)
= 9! / (5! * 4!)
= (9 * 8 * 7 * 6 * 5!) / (5! * 4 * 3 * 2 * 1)
= (9 * 8 * 7 * 6) / (4 * 3 * 2 * 1)
= 3024 / 24
= 126
So there are 126 combinations of 9 things taken 5 at a time.