In how many different ways can Alice Bob Carol Darla and Eva

In how many different ways can Alice, Bob, Carol, Darla and Evan all sit around a table? (If it helps you, an arrangement can be specified by starting at Alice and going clockwise around the table).

Solution

Given that Alice, Bob, Carol, Darla and Evan all sit around a table.

We will fix Alice to a position and we can arrange the remaining 4 in 4! Ways=4×3×2×1=24 ways

So the number of ways in which the 5 members can be arranged around a table is 24 ways.

If it is said that there shouldn\'t be common neighbors then it will be 4!/2=24/2=12 ways