1. In how many ways can 6 persons be arranged at a random table so that 2 particular persons may sit together?
Ans:
i) Arrange with respect to table: Taking 2 particular persons as one person, we are to arrange 5 (=1+4) persons in 5!. Again 2 persons can be arranged among themselves in 2! ways.
So required no. of arrangement = 5! x 2! =120 x 2=240
ii) Arrangement with respect to each other : At first 2 particular persons can be arranged themselves in 2! ways. Keeping them fixed & taking as one person, all the 5 persons can be arranged in (5-1)!=4! ways.
So required no. of ways=4! x 2!=24 x 2=48