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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Permutation and Combination

NDA 2023 · Mathematics · Permutation and Combination

Three boys, P, Q, R an three girls S, T, U are to be arranged in a...

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that all three boys sit together?

Options

  1. A15\frac{1}{5}
  2. B14\frac{1}{4}
  3. C13\frac{1}{3}
  4. D112\frac{1}{12}

Correct answer

A. 15\frac{1}{5}

Step-by-step solution

The number of ways in which all boys sit together =4!×3=4!\times 3 !  Required probability =4!×3!6!=15\text{ Required probability }=\frac{4!\times 3!}{6!}=\frac{1}{5}
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