Multiple choice

How many three letter words can be formed by using the letters of the word $'EQUATION'$ such that at least one vowel should be included in each word? (repetition of letters not allowed)

  1. $336$
  2. $6$
  3. $339$
  4. $330$
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D Correct answer
AI explanation

The word EQUATION has 5 vowels and 3 consonants, so the total number of 3-letter words possible without repetition is 8P3 = 8 factorial divided by 5 factorial = 336. The number of words containing only consonants (no vowels) is 3P3 = 3 factorial = 6. Subtracting the words with no vowels from the total gives 336 minus 6 = 330.

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