If $^{12}P_r = 1320$,then $r$ is equal to

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

How many triangles can be formed by joining four points on a circle?

$P, Q, R$ and $S$ have to give lectures to an audience. The organiser can arrange the order of their presentation in ............. ways.

There are $8$ students appearing in an examination of which $3$ have to appear in a Mathematics paper and the remaining $5$ in different subjects. In how many ways can they be made to sit in a row if the candidates in Mathematics cannot sit next to each other?

How many words can be made from the letters of the word $BHARAT$ in which $B$ and $H$ never come together?