Question

The letters of the word ORIENTAL are arranged in all possible ways. The chance that the consonants and vowels occur alternatively is

• A. $\frac{1}{70}$
• B. $\frac{2}{35}$
• C. $\frac{1}{35}$
• D. $\frac{4}{35}$

Answer 1

Answer: (C)

$\frac{1}{35}$

ORIENTAL has $4$ vowels and $4$ consonants,
There is only $2$ ways by which we could get consonants and vowels occur alternatively.
Total cases: $8!$
Favorable cases: $2\times 4!\times 4!$
$=\frac{2\times 4!\times 4!}{8!}$
$=\frac{1}{35}$