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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 persons between A and B is

A

4/45

B

8/45

C

1/5

D

1/210

Answer

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 x 8 !

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