This is similar to a problem i had in an old course where you had to find integers x,y,z s.t. x + y + z = some +ve integer.
So i think this one can be reworded as the 3 boxes being x,y and z. And n being 7 distinct objects.
Since you want +ve integers what to do is set x' = x-1 etc and then you get x' + y' + z' = 4.
This is done by using the binomial expression where k is the number of 'boxes'
So we get = 15.