Q:

Pairs of classmates

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

A:

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. 

