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Question: Fifteen persons among whom are A and B, sit down at random at a round table. The probability that th...

Fifteen persons among whom are A and B, sit down at random at a round table. The probability that there are 4 persons between A and B, is

A

13\frac { 1 } { 3 }

B

23\frac { 2 } { 3 }

C

27\frac { 2 } { 7 }

D

17\frac { 1 } { 7 }

Answer

17\frac { 1 } { 7 }

Explanation

Solution

Let AA occupy any seat at the round table. Then there are 14 seats available for B.

If there are to be four persons between AA and B.

Then has only two ways to sit, as show in the fig.

Hence required probability =214=17= \frac { 2 } { 14 } = \frac { 1 } { 7 }