two
252 teams.
if order does not matter then, (23x22x21x20x19)/(5x4x3x2x1) = 33,649
18
I figured out the answer: 18+7 = 25, So 25C5 = 53,130 Teams. This assumes there are no sex restrictions on the teams (for example, "teams must include at least one boy and at least one girl"). That would be a lot more complicated, and if that's a factor you'd need to specify exactly what the restrictions are.
two
Any 5 from 7 is (7 x 6)/2 ie 21.
252 teams.
C105 = 10 ! / (5!x(10-5)!) = 10! /5!2 = 252
75
6,375,600
if order does not matter then, (23x22x21x20x19)/(5x4x3x2x1) = 33,649
18
3 students can be chosen from a class of 30 in (30 x 29 x 28) = 24,360 ways.But each group of the same 3 students will be chosen in six different ways.The number of different groups of 3 is 24,360/6 = 4,060 .
There are 11880 ways.
1 team of 36 students 2 teams of 18 3 teams of 12 4 teams of 9 6 teams of 6 9 teams of 4 12 teams of 3 18 teams of 2 and 36 teams of 1
There are 10 different sets of teachers which can be combined with 4 different sets of students, so 40 possible committees.