The letters of the word ZOOLOGY are arranged in <strong>ALL</strong> possible ways. What is the probability that the consonants and vowels occur alternatively?

Explanation

The word ZOOLOGY has 7 letters, comprising 4 consonants (Z, L, G, Y) and 3 vowels (O, O, O). The total number of arrangements is \frac{7!}{3!} = 840. For vowels and consonants to alternate, the arrangement must follow the pattern C V C V C V C. The 4 consonants can be arranged in 4! = 24 ways, and the 3 identical vowels can be arranged in \frac{3!}{3!} = 1 way. The probability is \frac{24 \times 1}{840} = \frac{1}{35}.

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