Question 1123561
4 seniors: 
pick 4 seniors from 10: 10c4=210 ways.
pick 2 people from the rest (8+5+3)=16 ones: 16c2=120 ways.
Total: 210*120=25200 ways.

5 senoirs: 10c5*16c1=4032 ways.
6 seniors: 10c6=210 ways.

Add them all up:29442 ways. (I did not expect it to be that much though)
And we're done.