How many different ways can 5 people sit at a round table?

Answer 1

This question is entirely mathematical and i will answer it the best I can in terms that can be easily understood.

This scenario can be solved easily using a permutation, a permutation describes the arrangement of objects (or events) in a specific order.

For example: ABC is different to ACB, CAB, BAC, BCA and CBA.

Generally the number of ways of arranging r objects from a group of n objects is:

nPr Which equals n! divided by (n-r)!

Note: ! =factorial (4!=4x3x2x1, 8!=8x7x6x5x4x3x2x1) and so on

However in a circle we have a continuous loop where objects can be arranged. We must take into consideration the direction when dealing with circles.

If we differ between clockwise and anticlockwise then the reult would be (n-1)!

In this case it would (5-1)!=4!=24

However if no distinction is made between clockwise and anticlockwise then the result is (n-1)! divided by 2

Therefore the answer would be 4!/2=24/2=12

So 5 people can site around a table either 12 different ways, or 24 different ways depending on whether the direction is taken into consideration.