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Question: There are 10 persons among whom are A and B who are made to stand in a row in random order. The prob...

There are 10 persons among whom are A and B who are made to stand in a row in random order. The probability that there is exactly one person between A and B is-

A

445\frac { 4 } { 45 }

B

845\frac { 8 } { 45 }

C

15\frac { 1 } { 5 }

D

1210\frac { 1 } { 210 }

Answer

845\frac { 8 } { 45 }

Explanation

Solution

n (S) = total number of ways in which 10 persons can be made to stand = 10!

n (5) = Number of ways in which exactly one person stands between A and B = (10 – 2) . 2. (10 – 2)! = 16 × 8!

\ P(5) = 16×8!10!\frac { 16 \times 8 ! } { 10 ! } = 1610×9\frac { 16 } { 10 \times 9 }= 845\frac { 8 } { 45 }