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Question

Three persons A,B,C are to speak at a function along with 5 other persons. If the persons speak in random order, the probability that A speaks before B and B speaks before C is pq, where p,q are co-prime. Then p+q is 


Solution

Total number of ways in which 8 persons can speak is 8!

Number of ways in which A,B and C can be arranged in the specified speak order is 8C3×1 as the order of A,B,C is already fixed.
Remaining 5 persons can speak in 5! ways.
So the favourable number of ways =8C3×5!
Hence, required probability =8C3×5!8!=16

Mathematics

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