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

1/(5! ×4!)

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

1/9!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9/9!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
1/(5! ×4!)

There are 5 vowels and 4 consonants.

Total ways to arrange: $9!$

Vowels can be arranged in 5! ways out of which in 1/5! they are in alphabetical order.

Similarly for consonants.

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

Total ways: $9!$

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

Suggest Corrections

Similar questions

Q. If in the word FRACTION, first all the consonants are arranged in alphabetical order from left to right and then all the vowels are arranged in alphabetical order from left to right, which of the following is the fifth letter from the right?

How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?

– the vowels occur in the same order (EUAIO);

– the consonants occur in the same order(DCTN);

– no two consonants are next to each other.

How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?

– the vowels occur in the same order (EUAIO);

– the consonants occur in the same order(DCTN);

– no two consonants are next to each other.

Q. How many ways are there to arrange the letters of the word EDUCATION so that all the following three conditions hold?
- the vowels occur in the same order(EUAIO);
- the consonants occur in the same order(DCTN);
- no two consonants are next to each other.

A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is

Join BYJU'S Learning Program

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

The correct option is A 1/(5! ×4!) There are 5 vowels and 4 consonants. Total ways to arrange: 9! Vowels can be arranged in 5! ways out of which in 1/5! they are in alphabetical order. Similarly for consonants. Total Favorable ways: 9!(5!×4!) Total ways:9! P(E)=1(5!×4!)