Q108 / 120 · NDA 2024 (Phase 2) · Mathematics

The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

  • Correct answer
    A
    $\frac{6}{35}$
  • B
    $\frac{3}{35}$
  • C
    $\frac{2}{35}$
  • D
    $\frac{1}{35}$

Solution

Vowels $=0,0,0$ and consonant $=\mathrm{Z} \mathrm{L} \mathrm{G} \mathrm{Y}$ Number of words form from letters of word ZOOLOGY $=\frac{7!}{3!}$ $\therefore$ Number of words in which consonants and vowels occur alternatively $\mathrm{n}(\mathrm{E})$ $\begin{aligned} & =Z * L * G * Y=4!\times 3! \\ & \therefore P(E)=\frac{n(E)}{n(S)}=\frac{4!\times 3!\times 3!}{7!}=\frac{3 \times 2 \times 3 \times 2}{7 \times 6 \times 5}=\frac{6}{35} \end{aligned}$

Hence, the correct answer is option: 'A'.

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