Past paper questions

A queue is formed by 6 boys and 2 girls. If no girls are next to each other, how many different queues can be formed?

Bag $P$ contains $2$ red balls and $4$ green balls while bag $Q$ contains $1$ red ball and $3$ green balls. If a bag is randomly chosen and then a ball is randomly drawn from the bag, find the probability that a green ball is drawn.

Let $x_{1}$, $y_{1}$ and $z_{1}$ be the mean, the median and the variance of a group of numbers $\{a_{1}, a_{2}, a_{3}, \ldots, a_{50}\}$ respectively while $x_{2}$, $y_{2}$ and $z_{2}$ be the mean, the median and the variance of the group of numbers $\{a_{1}, a_{2}, a_{3}, \ldots, a_{49}\}$ respectively. If $x_{1} = a_{50}$, which of the following must be true?

I. $x_{1}=x_{2}$

II. $y_{1}\geq y_{2}$

III. $z_{1}\leq z_{2}$