Again six people, including A,B, and C, form a queue in a random order (all 6! orderings are equiprobable). Consider the event "B is between A and C in the queue". What is its probability? (The order of A and C can be arbitrary, but B should be between them)
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Given : Six People arrangements in Queue
To find : Probability that B is between A & C
Solution:
6 people can be arranged in 6 ! ways
now taking ABC as one and rest 3 hence
total 4
4 can be arranged in 4 ! ways
ABC can be arranged ABC or CBA in 2 ways
Hence total possible arrangements = 2 * 4 !
Probability that B is between A & C = 2 * 4 ! / 6!
= 2 / (6 * 5)
= 1/15
1/15 is the probability of the event that B is between A and C in the queue
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