Question

If the letters of the word 'MISSISSIPPI' are written down at random in a row, what is the probability that four S's come together.

Answer 1

Numbers of different letters can be written from 'MISSISSIPPI' is $\frac{11!}{4!4!2!}$

$=\frac{11\times 10\times 9\times 8\times 7\times 6\times 4\times 4!}{2!4!4!}=34650$

Now, 4S should come together, so considering it 1

We get,

$\frac{8!}{4!2!}=840$

[Different words when 4-S comes together]

$\therefore P\left(t\right)=\frac{840}{34650}=\frac{4}{165}$

$\therefore P\left(t\right)=\frac{4}{165}$