SOLUTION: if there is 8 empty seats on a bus and 5 people get on how many possible ways can they be seated?

Question 1028839: if there is 8 empty seats on a bus and 5 people get on how many possible ways can they be seated?
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:
if there are 8 empty seats on a bus and 5 people get on how many possible ways can they be seated?

Solution:
This is a problem of permutation, i.e. the number of possible arrangements (order counts) choosing 5 objects (seats) out of 8.
This is how it works:
The first person that gets on has 8 choices of seats.
The second person that gets on has 7 seats left.
...
The fifth person that get on has 4 seats to choose from.
This being a five-step experiment, we multiply the number of steps of each step, namely,
number of arrangements = 8*7*6*5*4 = 6720.

Once we identify the problem as permutation (of 5 out of 8), we can use the familiar formula
number of arrangements = nPr = 8P5 = 8!/(8-5)! = 40320/120 = 6720 as before.
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