Question

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How many different seating arrangements are possible for 6 people in 4 chairs?

Answer 1

360 ways

Explanation:

This is a permutation because we care about the order.

It is a seating arrangement, so order matters

We are taking 6 things 4 at a time

n!

--------- where n is the number of items and r is how many we are taking

(n-r)!

6!

------

(6-4)!

720

-------

2!

720/2

360 ways

Answer 2

Because the order doesn't matter on where each person sits use the combinations formula:

C = n! / (r!(n-r)!)

Where n is the total number of people and r is the number of chairs.

C = 6! / (4!(6-4)!)

C = (6*5*4*3*2*1) / ((4*3*2*1(2*1))

C = 720 / (24*2)

C = 720 / 48

C = 15

There are 15 different arrangements.