sandy wrote:

Six people are asked to sit down in a circle consisting of eight chairs.How many different ways are there to distribute the six people on the eight chairs?

The basic idea here is that, for each possible arrangement, if EVERYONE moves 1 seat to the right, we have the

same configuration.

Likewise, if EVERYONE moves 2 seats to the right, we have the same configuration.

Likewise, if EVERYONE moves 3 seats to the right, we have the same configuration.

.

.

.

Likewise, if EVERYONE moves 7 seats to the right, we have the same configuration.

So, one seating arrangement has

8 equivalent arrangements

At this point, let's NUMBER the 8 chairs as follows: #1, #2, #3, ..... #7 and #8

We'll call the six people A, B, C, D, E and F

Now seat each person.

We can place person A in one of 8 chairs

After that, we can place person B in one of the 7 remaining chairs

After that, we can place person C in one of the 6 remaining chairs

After that, we can place person D in one of the 5 remaining chairs

After that, we can place person E in one of the 4 remaining chairs

After that, we can place person F in one of the 3 remaining chairs

So, the number of arrangements = (8)(7)(6)(5)(4)(3)

HOWEVER, we're not quite done.

We have counted each equivalent seating

8 times

So, to account for this, we must divide (8)(7)(6)(5)(4)(3) by

8 to get: (8)(7)(6)(5)(4)(3)/

8 = (7)(6)(5)(4)(3) = 2520

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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