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Question: The letters of the word ‘ASSASSIN’ are written down at random in a row. The probability that no two ...

The letters of the word ‘ASSASSIN’ are written down at random in a row. The probability that no two S occur together is

A

135\frac { 1 } { 35 }

B

114\frac { 1 } { 14 }

C

115\frac { 1 } { 15 }

D

None of these

Answer

114\frac { 1 } { 14 }

Explanation

Solution

Total ways of arrangements.

Now ‘S’ can have places at dot’s and in places of w, x, y, z we have to put 2A’s, one I and one N.

Therefore, favourable ways =5C4(4!2!)= { } ^ { 5 } C _ { 4 } \left( \frac { 4 ! } { 2 ! } \right).

Hence, required probability =5.4!2!4!2!8!=114= \frac { 5.4 ! 2 ! 4 ! } { 2 ! 8 ! } = \frac { 1 } { 14 } .