To elaborate on Brian's post, the way he got the 7*6*5 can be thought up a little easier if you do a small diagram

I made mine like each - is a seat, since people cant sit in 2 seats, each time the amount of the people who can sit in a seat goes down.


       -     -     -     -     -     -     -     -                         
       8     7     6     5     4     3     2     1
            amount of choices left for each seat

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Basic linear algebra uncovers and clarifies very important geometry and algebra.

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