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Five people, designated as A, B, C, D, E, are
               arranged in linear order. Assuming that each possible
               order is equally likely, what is the probability
               that
                        (a) there is exactly one person between A and B?
                        (b) there are exactly two people between A
                             and B?
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3 Answers

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A)3 possiblities for character b/w A and B={C,D,E}----->3

  2 permutations of A and B= {AB,BA}-----2

  after placing one character b/w A and B ,and permuting them we have 3 elements left----->3!=6

      i)block formed by A,B and one character.

     ii) and iii) 2 characters left

Total=6*2*3=36

probablity=36/120=0.3

B)3 possiblities for character b/w A and B={CD,DE,CE}----->3

  2 permutations of A and B= {AB,BA}-----2

  after placing two character b/w A and B ,and permuting them we have 2 elements left----->2!=2

      i)block formed by A,B and two characters.

     ii) 1 character left

Total=2*2*3=12

probablity=12/120=0.1

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1 votes

(a)

Probability = $\begin{align*} &\frac{12+12+12}{5!} = \frac{35}{120} = 0.3 \end{align*}$


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