First slide

Theorems of probability

Question

The chance that the vowels are separated in an arrangement of the letters of the word "HORROR" is

Moderate

A

$\frac{1}{2}$
B

$\frac{2}{3}$
C

$\frac{3}{4}$
D

None of these

Solution

$Total number of ways of arranging HORROR = \frac{6!}{3! 2!} = 60$
$Number of ways in which vowels are separated = \frac{6!}{3! 2!} - \frac{5!}{3!}$
$= 40$
$Probability = \frac{40}{60} = \frac{2}{3}$

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