Question 169452
Think of it this way.
How many choices do you have for the first seat?  8 people, so 8 possibilities.
How many are left after the first person is in seat 1? 7 people
How many choices do you have for the second seat? 7 people, so 7 possibilities.
Keep doing this for each seat.
End result - 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 8!

have a look at this video for more examples of similar stuff
http://collabvsl.wetpaint.com/page/Basic+Probability