In how many ways can $n$ books be arranged in a row so that two specified books are not together?

$n$ 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:

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)

The number of ways in which an examiner can assign $30$ marks to $8$ questions,awarding not less than $2$ marks to any question is

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,seven of which lie on the same straight line,is