A kid can choose 7 out of 12 donuts to eat. How many ways can he do this if he must choose at exactly 3 of the first 5?
Similarly, how many combinations are there if he must choose at least 3 of the first 5.
The way I approached this is 5C3*9C4 if he must choose exactly 3 of the first 5, but for the second part where he must choose at least 3 of the first 5, I have 5C3*9C4+5C4*8C3+5C5*7C2. Is my reasoning correct?