Question 1168882: In how many ways can 4 guests sit down in 6 seats in a row so that the leftmost place will be used and the rightmost place will be empty?
Answer by Solver92311(821)   (Show Source):
You can put this solution on YOUR website!
There are 4 guests and the left-most seat must be occupied, so there are 4 ways to choose the occupant of that seat. Then, for each of those 4 ways, there are 4 ways to decide the occupant of the second seat -- the three remaining people plus the possibility of that seat being empty, for a total of 16 ways to decide the configuration of the first two seats. Then, for each of those 16 ways, there are three ways to choose the occupant of the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). 16 times 3 is 48. For each of those ways, there are two choices for the next seat, so 96, and then one choice for the fifth seat. So 96 ways.
John
My calculator said it, I believe it, that settles it
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