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

$\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} $

1 Answer

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.
answered Jul 8, 2014 by sreemathi.v

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