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Question: The letter of the word \`ASSASSIN' are written down at random in a row. The probability that no two ...

The letter 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 =8!2!⋅4!= \frac { 8 ! } { 2 ! \cdot 4 ! }

Now ‘S’ can have places at dot’s and in places of w,x,y,zw , x , y , z we have to put 2A′s2 A ^ { \prime } s one II and one

Therefore favourable ways =5(4!2!)= 5 \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 }