Letters of the word "EDUCATION" is arranged. What is the probability

Question -

Letters of the word "EDUCATION" is arranged. What is the probability that vowels and consonants are in alphabetical order?

Options:

A .

\frac{1}{(5! \times 4!)}

B .

\frac{1}{9!}

C .

\frac{9}{9!}

D . None of these.

Answer: Option A
:
A

There are 5 vowels and 4 consonants.

Total ways to arrange: 9!

Vowels can be arranged in 5! ways out of which in $\frac{1}{5!}$ they are in alphabetical order.

Similarly for consonants.

Total Favorable ways: $\frac{9!}{(5! \times 4!)}$

Total ways: 9!

P(E)= $\frac{1}{(5! \times 4!)}$

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