Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Probability

Question:

What is the probability that for S's come consecutively in the word `MISSISSIPPI'?

Options:

$\frac{1}{165}$

$\frac{2}{165}$

$\frac{4}{165}$

none of these

Correct Answer:

$\frac{4}{165}$

Explanation:

The total number of arrangements of the letters of the word 'MISSISSIPPI' is

$\frac{11!}{4!4!2!}$

Considering 4 S's as one letter, there are 8 letters which can be arranged in arrow in ways $\frac{8!}{4!2!}$ ways.

∴ Number of ways in which 4 S's come together = $\frac{8!}{4!2!}$

Hence, required probability $=\frac{8!/4!2!}{11!/4!4!2!}=\frac{8!×4!}{11!}=\frac{4}{165}$