A committee must be formed with 2 teachers and 6 students. If there are 8 teachers to choose from, and 16 students, how many different ways could the committee be made?

To solve this problem, we will use the concept of combinations in mathematics.

Step 1: Calculate the number of ways to choose 2 teachers from 8. This is a combination problem, which can be solved using the formula C(n, k) = n! / [k!(n-k)!], where n is the total number of options, k is the number of options to choose, and "!" denotes factorial.

So, the number of ways to choose 2 teachers from 8 is C(8, 2) = 8! / [2!(8-2)!] = 28.

Step 2: Calculate the number of ways to choose 6 students from 16. Again, this is a combination problem, so we use the same formula.

The number of ways to choose 6 students from 16 is C(16, 6) = 16! / [6!(16-6)!] = 4368.

Step 3: Multiply the results from step 1 and step 2 to get the total number of ways to form the committee.

So, the total number of ways to form the committee is 28 * 4368 = 122,304.

Therefore, there are 122,304 different ways to form the committee.