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.

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Solution

The correct option is A
15

Vowels can be arranged in one way.

There will be $6$ gaps around them. We need $4$ gaps as the arrangement can be done in one way.

Therefore, $^{6} C_{4} = 15$

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Similar questions

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.

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 are next to ea ch other (DCTN)
- no two consonants are next to each other.

In how many ways can the letters of the word EDUCATION be rearranged so that the relative position of the vowels and consonants remain the same as in the word EDUCATION?

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

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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.

The correct option is A 15 Vowels can be arranged in one way. There will be 6 gaps around them. We need 4 gaps as the arrangement can be done in one way. Therefore, 6C4=15

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.

The correct option is A
15

Vowels can be arranged in one way.

There will be $6$ gaps around them. We need $4$ gaps as the arrangement can be done in one way.

Therefore, $^{6} C_{4} = 15$