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?

No, of mathematics papers = 9
(i) The best and the worst may come together:-
Consider the 2 papers best and worst papers are taken as a unit and the remaining 7 papers
are 7 units
$\therefore$ 1 unit + 7 papers = 8 units
These 8 units can be arranged in 8! ways and 1 unit of 2 papers can be rearranged among themselves in 2! ways
$\therefore$ Req. no. of arrangements = 8! × 2!
(ii) The best and the worst may not come together:-
First we arrange the remaining 7 papers in a row in 7! ways then there are 8 gaps among them. Thus we have 8 gaps and 2 papers are
arranged in ${}^{8}P_2$ ways
$\therefore$ Req. no. of arrangements 8 $=7!\times {}^{8}P_2$