In how many ways 9 mathematics papers can be arranged so that the best and the worst (i) may come together (ii) may not come together ?

Explanation

i) If the best and worst papers are treated as one unit, then we have 9-2+1=7+1=8 papers. Now these can be arranged in (7+1)! Ways and the best and worst papers between themselves can be permuted in 2! Ways. Therefore the number of arrangements in which best and worst papers come together is 8! 2!.
ii) Total number of ways of arranging 9 mathematics papers is 9!. The best and worst papers come together in 8! 2! ways. Therefore the number of ways the may not come together is `9!-8! 2!=8! (9-2)=8!xx7`.