A class of 16 students contains five Math majors

First, you need to know the formula for how many combinations can be made from a group of stuff. The formula is n!/(n-i)!/i! where n is the number of things and i is how many you are taking at a time.

With that in mind, here is how you do A)
- There are five ways to have exactly one math major
- There are 11 other students to fill the other two spots, so there are 11!/9!/2! ways to do that = 55
- The answer is 5x55 = 275

B)
- Three math majors would be 5!/2!/3! = 10
- Three engineering majors would be 7!/4!/3! = 35
- Three Physics majors would be 4!/1!/3! = 4
- The sum of those is 49

you are awesome, thanks!