Question

8 friends are going out to dinner. there are two circular tables of 4 available. If A and B must not sit at the same table, C and A must sit at the same table, but must not be sitting beside each other, in how many ways can the friends all sit down for dinner?

Answer 1

If A and B must not sit at the same table, C and A must sit at the same table, then number ways they can be placed on 2 different tables is 2.

Once placed, number of ways 4 people on a circular table can be arranged in (4-1)! = 3! = 6 ways.

Suppose C and A sit together (treated as one unit), number of ways 3 people on a circular table can be arranged in (3-1)! = 2!= 2 ways.

So, number of ways 4 people on a circular table can be arranged such that C and A must not be sitting beside each other

= 6 - 2 = 4 ways

Total number of ways = Number of ways A, B and C are placed on 2 different tables * Number of ways 4 people on a circular table can be arranged such that C and A must not be sitting beside each other * Number of ways 4 people (including B) on a circular table

= 4 * 6 * 2

= 48 ways