In how many ways can 7 examination papers be arranged so that papers 6 and 7 are never together?

In how many ways can 7 examination papers be arranged so that paper 1 and paper 2 never come toghether?

In how many ways can 10 examination papers be arranged so that the best and the worst papers never come together?

In how many ways can five examination papers be arranged so that Physics and Chemistry papers never come together?

In how many ways can 7 people be arranged at round table, so that two particular persons be together?

In how many ways can 5 keys be put in a ring?

In how many ways can 5 different books be arranged on a shelf if (i) there are no restrictions (ii) 2 books are always together (iii) 2 books are never together

In how many ways can 13 billiard balls be arranged, if 6 of them are green, 4 red and 3 black?

Six men and five women sit around a table. In how many ways can they seat themselves so that no two ladies are together?