Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the height of the tallest person selected when three people are randomly chosen from a group of $10$.

Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the number of girls selected when two children are chosen at random from a group containing one girl and three boys.

Give a reason why a binomial distribution would not be a suitable model for the distribution of $X$ in the following situation,

$X$ is the number of motorbikes selected when four vehicles are randomly picked from a car park containing $134$ cars, $17$ buses and nine bicycles.

The variable $Q~B\left(n,\frac{1}{3}\right)$ , and its standard deviation is one-third of its mean. Calculate the non-zero value of $n$ and find $P(5<Q<8)$.

The random variable $H~B(192,p)$, and $E\left(H\right)$ is $24$ times the standard deviation of $H$. Calculate the value of $p$ and find the value of $k$, given that $P(H=2)=k\times 2^{-379}$.

It is estimated that $1.3\%$ of the matches produced at a factory are damaged in some way. A household box contains $462$ matches. Calculate the expected number of damaged matches in a household box. 

It is estimated that $1.3\%$ of the matches produced at a factory are damaged in some way. A household box contains $462$ matches. Find the variance of the number of damaged matches and the variance of the number of undamaged matches in a household box.[Write your answer correcting to three decimal places]

It is estimated that $1.3\%$ of the matches produced at a factory are damaged in some way. A household box contains $462$ matches. Show that approximately $10.4\%$ of the household boxes are expected to contain exactly eight damaged matches.

It is estimated that $1.3\%$ of the matches produced at a factory are damaged in some way. A household box contains $462$ matches. Calculate the probability that at least one from a sample of two household boxes contains exactly eight damaged matches.  [Write your answer correcting to three decimal places]