There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.
There are 4 guests and the leftmost seat is to be occupied, so there are 4 such ways to choose the occupant of that seat.
Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.
Then, for each of those 16 ways, there are 3 ways to choose the occupant for 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). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.
Read more about Permutations and combinations:
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