Final answer:
There are 252 different 5-element subsets that can be formed from a set with 10 elements (A, B, C, D, E, F, G, H, I, J), calculated using the combination formula C(n, k) = n! / (k!(n-k)!).
Step-by-step explanation:
The question asks about the number of 5-element subsets that can be formed from a set with 10 elements (A, B, C, D, E, F, G, H, I, J). This is a problem of combinatorics, specifically concerning combinations, which are ways of selecting items from a collection, such that the order of selection does not matter.
To calculate the number of 5-element subsets from a 10-element set, we use the combination formula:
C(n, k) = n! / (k!(n - k)!)
Where n is the total number of items, k is the number of items to choose, n! is the factorial of n, and k! is the factorial of k. Plugging in the values for our problem:
C(10, 5) = 10! / (5! × (10 - 5)!) = 252
Therefore, the set with elements A, B, C, D, E, F, G, H, I, J has 252 different 5-element subsets.