A committee of 10 members sits around a table. Find the number of arrangements that have the president and the vice-president together.
Here, n = No. of committee members = 10
Consider 'President' and 'Vice-President' as one unit.
So there are 1 + 8 = 9 members to be arranged around a table.
Such arrangements are (9 – 1)! = 8! and corresponding to each of these 8! arrangements, the President and the Vice-President can interchange their places in 2! ways.
∴ the total number of circular arrangements of 10 committee members in which President and Vice-President sit together
= 8! × 2!