How many distinct groups of 5 possible from 10 seniors and 6 freshman? A school is forming a group of 5. There are 10 freshman and 6 seniors, and the group must have at least 2 freshman and at least 1 senior. How many distinct groups are possible?
My approach (that I think is definitely flawed) - 
This would be a combination problem because order does not matter. There has to be at least 2 freshmen and 1 senior so there are only 2 open spots left with a pool of 8 freshmen and 5 seniors, or 13 people. Would it just be C(13,2) or 13!/(2*11!)?

As you say the order doesn't matter. Then you have to think of all allowed groups, that is 2 freshmen 3 seniors, 3 freshmen 2 seniors, and 4 freshmen 1 senior. 
2 freshmen 3 seniors:
$\dfrac{10 \cdot 9}{2!} \cdot \dfrac{6 \cdot 5 \cdot 4}{3!} = \dfrac{10!}{2!(10-2)!}\cdot \dfrac{6!}{3!(6-3)!} = 900 $  possible combinations
3 freshmen 2 seniors:
$\dfrac{10 \cdot 9 \cdot 8}{3!} \cdot \dfrac{6 \cdot 5}{2!} = \dfrac{10!}{3!(10-3)!}\cdot \dfrac{6!}{2!(6-2)!} = 1,800 $  possible combinations
4 freshmen 1 senior:
$\dfrac{10 \cdot 9 \cdot 8 \cdot 7}{4!} \cdot 6 = \dfrac{10!}{(10-4)!4!}\cdot \dfrac{6!}{1!(6-1)!} = 1,260 $  possible combinations
TOTAL: 
Therefore, in total, there are $3,960$ possibilities 
