Question

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)

Answer 1

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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