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Question: Three numbers are selected at random from the set {1, 2, 3……N}, one by one without replacement. If ...

Three numbers are selected at random from the set

{1, 2, 3……N}, one by one without replacement. If the first number is known to be smaller than second, then the

probability that third selected number lies between the first

two numbers is

A

12\frac { 1 } { 2 }

B

13\frac { 1 } { 3 }

C

16\frac { 1 } { 6 }

D

18\frac { 1 } { 8 }

Answer

16\frac { 1 } { 6 }

Explanation

Solution

For any three numbers that are selected, they could have been arranged in ⨆\bigsqcup = 6 ways. Out of which there is only one favorable way. Hence required probability = 16\frac { 1 } { 6 }