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