If the best and the worst paper never appear together, find in how many ways six examination papers can be arranged.

There are 10 examination papers for a course. i. Find out in how many ways these examination papers can be arranged. ii. Find out in how many ways these papers can be arranged so that two papers must be consecutive. iii. Find out in how many was these papers can be arranged so that two particular papers should not be consecutive.

(i) How many words can be formed with the letters of the word 'FAILURE', if A and F are always together? (ii) In how many ways can 6 question papers be arranged if the best and worst papers are always together?

In how many ways ‘n’ objects can be arranged together in a line?

In how many ways can 12 papers be arranged if the best and the worst paper never come together?

Six students are contesting the election for the presidentship of the students' union. In how many ways can their names be listed on the ballot papers?