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 n_{1}, n_{2}, ..., n_{k} objects in each group, where n_{1} + n_{2} + ... + n_{k} = n. The number of ways to do this is equal to (n!) / [(n_{1}!) × (n_{2}!) × ... × (n_{k}!)], 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 n_{1} = 6, n_{2} = 3, n_{3} = 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.