Verified answer

This is equivalent to giving €3 to every student, then taking €2 back.

We could take €2 from one student, there are 6 ways of doing that, since there are 6 students.

Or we could take €1 from two different students, we have 6 choices for the first student, 5 choices for the second student making a total of 6x5 = 30 ways. However the order we choose the students is irrelevant (e.g picking student 1 then 3 is equivalent to picking 3 then 1), so we have to divide by 2. There are 15 ways of taking €1 from two different students.

Overall there are 6+15 = 21 ways to distribute the coins.

3-3-3-3-3-1 : 6!/5! = 6 ways

3-3-3-3-2-2 : 6!/(4!2!) = 15 ways

add up to get ans = 21 <------