Question

Submit a full solution (your final answer AND your work) to the problem below.

In how many ways can a professor group 10 students into 5 teams of 2? In this case, we should assume that pairing Ann and Bob together is the same as pairing Bob with Ann, so we do not need to pay attention to the ordering here, and we should not "double-count" these sorts of cases.

Answer 1

Answer: Your welcome!

Explanation:

There are a total of 45 ways to group 10 students into 5 teams of 2. This is because the total number of combinations can be calculated as 10!/(2!*2!*2!*2!*2!) = 45. This is because 10! represents the total number of unique permutations of the 10 students and the 5 2! terms in the denominator represent the number of unique permutations for each of the 5 teams of 2. Therefore, the total number of unique combinations of the 10 students into the 5 teams of 2 is 45.