What is the probability that no two girls sit together?

Consider the following for the next five (05) items that follow: Three boys P, Q, R and three girls S, T, U are to be arranged in a row for a group photograph.

  1. A. \frac{2}{5}
  2. B. \frac{3}{5}
  3. C. \frac{1}{18}
  4. D. \frac{1}{5}

Correct Answer: D. \frac{1}{5}

Explanation

First, arrange the 3 boys in 3! = 6 ways. This creates 4 possible gaps for the girls (including the ends): \_ B \_ B \_ B \_. The 3 girls can be placed in these 4 gaps in {}^4P_3 = 24 ways. Total favorable outcomes = 6 \times 24 = 144. The probability is \frac{144}{720} = \frac{1}{5}.

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