A bag contains 4 red and 6 green gumballs. if you select 5 of them without looking, how many ways can you get exactly 3 red or exactly 2 green gumballs?

This is a combination problem. The approach to this is by using the nCr method, where n is the number of total objects and r is the number of success. For example, if you want to get 3 red out of the total 4, then that would be 4C3. That means,

4C3 = 4!/3! (4 - 3) ! = 4 ways

If you want to get 2 green out of the total 6, then that would be 6C2. That means,

6C2 = 6!/2! (6-2) ! = 15 ways

Therefore, there are a total of 4+15 = 19 ways.