From a lot of 12 items containing 3 defectives, a sample of 5 items is drawn at random. Let the random variable $$X$$ denote the number of defective items in the sample. Let items in the sample be drawn one by one without replacement. If variance of $$X$$ is $$\frac{m}{n}$$, where $$\operatorname{gcd}(m, n)=1$$, then $$n-m$$ is equal to _________.

From a lot of 10 items, which include 3 defective items, a sample of 5 items is drawn at random. Let the random variable $$X$$ denote the number of defective items in the sample. If the variance of $$X$$ is $$\sigma^2$$, then $$96 \sigma^2$$ is equal to __________.

In a tournament, a team plays 10 matches with probabilities of winning and losing each match as $$\frac{1}{3}$$ and $$\frac{2}{3}$$ respectively. Let $$x$$ be the number of matches that the team wins, and $y$ be the number of matches that team loses. If the probability $$\mathrm{P}(|x-y| \leq 2)$$ is $$p$$, then $$3^9 p$$ equals _________.

A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics and Chemistry. It was found that all students passed in atleast one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, atmost 11 students passed in both Mathematics and Physics, atmost 15 students passed in both Physics and Chemistry, atmost 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is _________.