14.Probability
hard

શબ્દ $‘ASSASSIN'$ ના મુળાક્ષરોને એક હારમાં લખાવમાં આવે તો  $S$ પાસપાસે ન આવે તેની સંભાવના મેળવો.

A

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

B

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

C

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

D

એકપણ નહિ.

(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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