# How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time?

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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?

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There are 5 vowels and 3 consonants. 2 groups formed, one with vowels and other with consonants.

So those 2 groups can be arranged in 2! ways.

Now vowels in themselves can be arranged in 5! ways and consonants in themselves can be arranged in 3! ways.

So totally we have 2! * 5! * 3! ways i.e., 2*1*5*4*3*2*1*3*2*1 = 1440 ways