How many arrangements can be made of the letters of the word '$ARRANGEMENT$'?

In the given figure,$6$ '$A$'s should be written in such a manner that every row contains at least one '$A$'. The number of ways this is possible is:

Choose the correct number of ways in which $15$ different books can be divided into five heaps of equal number of books.

There are $6$ multiple choice questions on an examination. How many sequences of answers are possible,if the first three questions have $4$ choices each and the next $3$ have $5$ each?

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

There are $3$ different rings to be worn in four fingers with at most $1$ in each finger. In how many ways can this be done?