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Question
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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Solution
In the word EQUATION, there are 5 vowels, namely, A, E, I, O, and U, and 3 consonants, namely, Q, T, and N.
Sequence of vowel letters = 5! = 5 x 4 x 3 x 2 x 1 = 120
Sequence of consonant letters = 3! = 3 x 2 x 1 = 6
Vowels and letters can be written in 2 ways, take vowels first or take consonants.
Words formed from the letters of the word EQUATION when vowels and consonants come together
120 x 6 x 2 = 1440
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