If the letters of the word ASSASSINATION are arranged at random.Find the probability that four S's come consecutively in the word.

Question

$\begin{array}{1 1}(A)\;\large\frac{3}{143}\\(B)\;\large\frac{2}{143}\\(C)\;\large\frac{4}{143}\\(D)\;\large\frac{9}{143}\end{array} $

Answer 1

Step 1:

Given the word ASSASSINATION

Four S's come consecutively in the word

$\therefore$ Let us consider all 4 'S' together as 1 letter where by 4 'S' can be arranged in 4! ways.

If 4 'S' are considered to be a single letter then total number of letters is 10.

Sample space S=13!

Step 2:

$\therefore$ Four S's come consecutively in the word $=\large\frac{10!}{13!}$$\times 4!$

$\Rightarrow \large\frac{2}{143}$

Hence (B) is the correct answer.