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NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2024 · Mathematics · Permutation and Combination

The letters of the word ZOOLOGY are arranged in all possible ways....

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

Options

  1. A635\frac{6}{35}
  2. B335\frac{3}{35}
  3. C235\frac{2}{35}
  4. D135\frac{1}{35}

Correct answer

A. 635\frac{6}{35}

Step-by-step solution

Vowels =0,0,0=0,0,0 and consonant =ZLGYNumberof=\mathrm{Z} \mathrm{L} \mathrm{G} \mathrm{Y}Number ofwords form from letters of word ZOOLOGY =7!3!\frac{7!}{3!}\thereforeNumberofwordsinwhichconsonantsandvowelsoccuralternativelynof words in which consonants and vowels occur alternatively \mathrm{n}(E)\mathrm{E})=Z∗L∗G∗Y=4!×3!∴P(E)=n(E)n(S)=4!×3!×3!7!=3×2×3×27×6×5=635\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}$
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