We have the following:
The first chair can be any of the 15.
For each of those ...
The second chair can be any of the 14.
For each of those ...
And so on until choosing 8 chairs
.
.
.
The eighth chair can be any of 8.
For each of those ...
Number of ways to fill the 8 chairs = (15 x 14 x 13 x 12 x 11 x 10 x 9 x 8) = 259,459,200
But in each group of 8 people you can sit on (8 x 7 x 6 x 5x 4 x 3 x 2 x 1) = 40,320 orders.
So each group of 40,320 people is represented 24 times out of 259,459,200
Therefore, the answer is:
[tex]\frac{259459200}{40320}=6435[/tex]6435 sets of 8 members, in any order.
