Question 1119602
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Here is another way to solve the problem.<br>
(1) Place James, Esther, and John in the proper order.
(2) Have the 4th person choose a place in the line.  With 3 people currently in the line, there are 4 choices for where he can stand (left of James, between James and Esther, between Esther and John, or right of John).
(3) Now there are 4 people in line; the 5th person has 5 choices of where to stand in the line.
(4) Now there are 5 people in the line; the last person has 6 choices of where to stand in the line.<br>
The total number of different arrangements with the given restrictions is the product of the numbers of choices the last three people had for where to stand in the line: 4*5*6 = 120.