Question

A circular, rotating serving tray has 6 different desserts placed around its circumference. How many different ways can all of the desserts be arranged on the tray?
a.
120
c.
720
b.
5040
d.
30

Answer 1

@Mr.Man420

Answer 2

SAme as the last time I showed you. To find how many combinations there are you take the amount you have in this case 6 and you multiply t out. 6x5x4x3x2x1=?

Answer 3

720

Answer 4

Correct.(:

Answer 5

Let's consider the simpler case above in the figure.
You have 3 desserts to arrange in a circular plate. The plate rotates, so no dessert is assigned to the top spot or one of the lower spots in the plate. The only thing that matters are the relative positions of the desserts in the plate.

Answer 6

If the answer were 3!, you'd get 3! = 3 * 2 * 1 = 6.
Notice the 6 different outcomes above in the figure.

Answer 7

The problem is that since we are only concerned with the relative positions of the desserts in each plate, there are many repeats.

Answer 8

Plates A, C, and F are the same.
Plates B, D, and E are the same.
That means that, in fact, there are only 2 unique arrangements.

Answer 9

So was I wrong?

Answer 10

no you got it right

Answer 11

In this situation of a "circular permutation", the number of permutations is really (n - 1)!, not n!.
Notice that (3 - 1)! = 2! = 2, which is the answer for my simple example.
Similarly, the answer to you question is 5! = 120, not 6! = 720.

Answer 12

Ok, just checking.

Answer 13

Yes.

Answer 14

Your answer is correct for an arrangement in a row, not for a circular arrangement.

Answer 15

That's why it didn't work for your other question @Junie.Michell98

Answer 16

yeah

Answer 17

Notice that for an arrangement in a row, all 6 arrangements are different.
Here the number of different arrangements is indeed n!, as 3! = 6.