Multiple choice

The number of words of six letters containing equal number of vowels and consonants, repetition being allowed is

  1. $1157625$
  2. $7452000$
  3. $4200152$

  4. none of these
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A Correct answer
AI explanation

A six-letter word with equal vowels and consonants requires 3 vowels and 3 consonants. The 3 positions for vowels can be chosen in 6C3 ways, which equals 20. Since there are 5 vowels and 21 consonants in the English alphabet, and repetition is allowed, the number of words is 20 multiplied by 5 cubed multiplied by 21 cubed, which equals 1157625.

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