Seven people sit in a circle. How many ways can this be done if two people A and B sit together ​

Step-by-step explanation:

Suppose the persons are a, b, c, d, e, f and g.

Let us also assume that a and b always sit together.

Let us then put the remaining 5 persons in a circular arrangement. It can be done in (5–1)! = 4! = 24 ways. Now, the pair (a,b) can be placed between any two persons already placed in circular order. There are 5 such gaps. Finally the pair (a,b) can be placed in two ways viz. (a,b) and (b,a).

So, total number of ways a group of 7 persons can be seated around a circular table where 2 specified persons always sit together is 24 X 2 X 5 = 240

squares, rhombus, rectangles