Question 1119156: there are 6 people who will sit in a row but out of them james will always be left of of esther and john will always be right of esther. in how many ways can such arrangement be done?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! james immediately to the left of esther and john immediately to the right of esther form a block of 1.
therefore, instead of 6 elements, you have 4.
4! = 4 * 3 * 2 * 1 = 24.
there are 24 possible different arrangements of the 6 people.
name the people a,b,c,d,e,f.
let d = james.
let e = esther.
let f = john.
d,e,f form one block that we'll call g.
the number of groups of people that need to be arranged are now a,b,c,g.
that's 4!
the number of possible arrangements are shown in the following excel spreadsheet printout.
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