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i have found following problem in my combinatorics book.

The superintendent of the Hardluck Elementary School District suggests that the Board of Education meet a $5$ million(dollar) budget deficit by raising average class sizes, from $30$ to $36$ students, a $20$% increase. A district teacher objects, pointing out that if the proposal is adopted, the potential for a pair of classmates to get into trouble will increase by $45$%. What is the teacher talking about?

i am trying to imagine what is proposal of problem,first line states that if number of pupil increases by 6,then there would be $5$ million dollar deficit ,also number of pair classmates which get in trouble would increases by $45$%,so if for $30$ children,pair of classmates in trouble is about x quantity,then for $36$,it would be $x+0.45*x$,but how is this related to combinatorics?please help me

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    but does there exist solution generally of this problem?2012-06-30

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Combinatorics tells you how many pairs of students there are. In a class of 30, there are 435 pairs of students; in a class of 36, there are 630 pairs of students. Presumably, 630 is a 45 percent increase on 435.

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    *That's* where combinatorics comes in. You are choosing 2 students from 30. There are 30 ways to choose the first student, and for each of these 30 ways, there are 29 ways to choose the second student, so, all told, $30\times29=870$ ways to get the job done. But we've counted choosing Gauss then Euler as different from choosing Euler then Gauss, and since we're only interested in who the two students are and not in the order in which we chose them, we have to divide by 2. $870/2=435$.2012-06-30