Multiple choice

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

  1. $\displaystyle 105^2$
  2. $\displaystyle 210 \: \times \: 243$
  3. $\displaystyle 105 \: \times \: 243$

  4. none of these
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B Correct answer
AI explanation

A four-letter word must contain exactly two vowels and two consonants, with repetition allowed. The 2 positions for vowels can be chosen in 4 C 2 ways, and the two vowels can be selected and repeated in 5 squared ways. The two consonants can be selected and repeated in 21 squared ways, making the total calculations 6 multiplied by 25 multiplied by 441. This product equals 210 multiplied by 243.

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