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Question: The chance that the vowels are separated in an arrangement of the letters of the word “HORROR” is :...

The chance that the vowels are separated in an arrangement of the letters of the word “HORROR” is :

A

½

B

2/3

C

¾

D

None

Answer

2/3

Explanation

Solution

Total number of ways of arranging HORROR

= 6!3!2!\frac { 6 ! } { 3 ! 2 ! } = 60 Number of ways in which vowels are separated

= 6!3!2!\frac { 6 ! } { 3 ! 2 ! }– 5!3!\frac { 5 ! } { 3 ! } = 40

Probability = 4060\frac { 40 } { 60 } =