A formula for the number of possible combinations of r objects from a set of n objects is

C(n, r) = n!/(r!(n - r)!)

C(n, r) = 15

n = 6

r = ?

6!/(r!(6 - r)!) = 15

r!(6 - r)! = 6!/15

6! = 1*2*3*4*5*6 = 720

r!(6 - r)! = 720/15

r!(6 - r)! = 48

48 = 2*2*2*2*3

1<=r<=6

for r = 1 we have (6-1)! = 5! is dividable by 5 while 48 is not thus r is not 1

for r = 2 we have

2!(6-2)! = 2*4! = 2*2*3*4 = 48

r = 2 is a solution

for r = 3

3!(6 - 3)! = 2*3*2*3 = 36 thus r is not 3

for r = 4

4!(6 - 4)! = 2*3*4*2 = 48

r = 4 is a solution

for r = 5 the left side of 5!(6 - 5)! = 48 is dividable by 5 while the right is not so r is not 5

There are 15 ways to make combinations of 2 objects from a set of 6 objects.

There are 15 ways to make combinations of 4 objects from a set of 6 objects.