How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

Asked by Abhisek | 1 year ago |  74

##### Solution :-

There are 5 vowels i.e. A, E, I, O and U and 3 consonants i.e. Q, T and N.

Since, vowels and consonants occur together, both (AEIOU) and (QTN) can be considered as single objects.

Thus, there are 5! Permutations of 5 vowels taken all at a time and 3! permutations of 3 consonants taken all at a time.

Therefore, by multiplication principle, the number of words

$$2!\times 5!\times 3!= 1440 .$$

Answered by Pragya Singh | 1 year ago

### Related Questions

#### How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

How many words each of 3 vowels and 2 consonants can be formed from the letters of the word INVOLUTE?

#### Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

Find the number of permutations of n distinct things taken r together, in which 3 particular things must occur together.

#### How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’,

How many words, with or without meaning can be formed from the letters of the word ‘MONDAY’, assuming that no letter is repeated, if

(i) 4 letters are used at a time

(ii) all letters are used at a time

(iii) all letters are used but first letter is a vowel ?