Ryan B. answered 02/09/22
10+ Years Experience Tutoring - Master of Science in Mathematics
This problem is solved using the multinomial coefficient:
Suppose we have n interchangeable objects and k groups to put them in; we put n1, n2, ..., nk objects in each group, where n1 + n2 + ... + nk = n. The number of ways to do this is equal to (n!) / [(n1!) × (n2!) × ... × (nk!)], which is know as the multinomial coefficient.
Here, we have n = 17 employees (which are interchangeable because each employee has the same qualifications/skills) and k = 3 groups to put them in. We also have n1 = 6, n2 = 3, n3 = 8 (note that 6 + 3 + 8 = 17). Therefore, the number of teams that can be chosen is (17!) / [(6!) × (3!) × (8!)], which turns out to be 2,042,040.