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## Homework Statement

Either People of different heights are to be seated in a row. The shortest and tallest in this group are not seated at either end. What is the probability that:

a) the tallest and shortest persons are sitting next to each other? (Ans: 1/3)

b) there is one person sitting between the tallest and shortest? (Ans: 4/15)

## Homework Equations

combinations, permutations, factorials

## The Attempt at a Solution

i didnt even b cuz i dont get a. here is my solution for part a:

_ _ _ _ _ _ _ _ are the seats. the tallest and shortest cant be at the ends, so that leaves 6

_ _ _ _ _ _. the number of ways the tallest and shortest can sit together is:

(4!)(2) for the tallest/shortest person sitting in the middle 4 seats, and the other one is going to be on the seat that is left or right of the first 1. This added with 2 for the ends of this section of 6.

the number of ways the the above scenario can happen is: 6! (for the tallest/shortest) X 5! (for the other one) X 6! (for the rest of the people)

therefore the total probability for part a is: [(4!)(2) + 2]6! divided by 6!5!6! = 1/864, but thats wrong :/