How many distinct arrangements of the letters in the word $\mathrm{STATISTICS}$ are there?

Three skirts, four blouses and two jackets are hung in random order on a clothes rail. Find the probability that:

the three skirts occupy the middle section of the arrangement

Three skirts, four blouses and two jackets are hung in random order on a clothes rail. Find the probability that:

the two iackets are not separated.

A small library holds $1240$ books: $312$ of the $478$ novels $\left(N\right)$ have hard covers $\left(H\right),$ and there are $440$ books that do not have hard covers. Some of this information is shown in the Venn diagram opposite.

Find the value of $a,$of $b$ and of $c.$

A small library holds $1240$ books: $312$ of the $478$ novels $\left(N\right)$ have hard covers $\left(H\right),$ and there are $440$ books that do not have hard covers. Some of this information is shown in the Venn diagram opposite.

A random selection of $25$ of these books is to be donated to a charity group. The charity group hopes that at least $22$ of the books will be novels or hard covers. Calculate the probability that the charity group gets what they hope for.