Letter of word ` ASSASSIN ' are written down at random in a row. probability that no two S occur

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14.Probability

hard

The letter of the word `$ASSASSIN$' are written down at random in a row. The probability that no two $S$ occur together is

A

$\frac{1}{{35}}$

B

$\frac{1}{{14}}$

C

$\frac{1}{{15}}$

D

None of these

(IIT-1983)

Solution

(b) Total ways of arrangements $ = \frac{{8\,!}}{{2\,!\,\,.\,\,4\,!}}$

$ \bullet \,w \bullet x \bullet y \bullet z \bullet $

Now ‘$S$’ can have places at dot’s and in places of $w,\,\,x,\,\,y,\,\,z$

we have to put $2\,A's,$ one $I$ and one $N.$

Therefore favourable ways $ = 5{\rm{ }}\left( {\frac{{4\,!}}{{2\,!}}} \right)$

Hence required probability $ = \frac{{5\,.\,4\,!\,\,2\,!\,\,4\,!}}{{2\,!\,\,8\,!}} = \frac{1}{{14}}.$

Standard 11

Mathematics

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