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?

Question

Filo · Accepted Answer

we have to separate the consonants and vowels and consider each time the set of the consonants and vowels as a single letter.

now,

here, word is E Q U A T I O N

vowels —> E , U, A , I , O ( there are five vowels in given words )

consonants—> T, Q , N ( there are 3 consonants in given words )

the vowels can be arranged in

5!

ways

the consonants can be arranged in

3!

ways

These vowels and consonants ( when we take as a single letter )can be arranged

2!

ways .

hence, a/c to fundamental principle of counting

total number of ways

= 5! \times 3! \times 2!

= (5 \times 4 \times 3 \times 2) \times (3 \times 2) \times (2)

= 120 \times 6 \times 2

= 1440

Question Text	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?
Answer Type	Text solution:1
Upvotes	150

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?

Text solutionVerified

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