Total number of ways 6 ppl can be arranged in a circle - 5! = 120
A) if a and b are always together - 4! = 24 x 2 = 48 ways
B) if they are separated - 120 -48 = 72 ways.
when arranging items in a row , the total ways to arrange them is n!, but when arragning items in a circle the formula becomes (n-1)!.
since we have six people then (6-1)! = 120
now note that two people have to sit together - making then as one, so (5-1)! = 24
I don't understand why you are multiplying the outcome in 2. can you please explain ?
I think that the answer is 24 ways for (A).