A set has 9 elements. How many of its subsets have 6 elements
To find the number of subsets that have 6 elements, we need to choose 6 elements out of the 9 elements in the set.
The number of ways to choose 6 elements out of 9 is given by the combination formula:
C(n, k) = n! / (k! * (n-k)!)
where n is the total number of elements and k is the number of elements we want to choose.
Plugging in the values, we find:
C(9, 6) = 9! / (6! * (9-6)!)
= 9! / (6! * 3!)
= (9 * 8 * 7 * 6 * 5 * 4 * 3!)/(6 * 5 * 4 * 3 * 3!)
= (9 * 8 * 7) / (3 * 2 * 1)
= 3 * 4 * 7
= 84
Therefore, there are 84 subsets with 6 elements in a set of 9 elements.