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MHT CET202527 Apr 2025Evening ShiftMathematicsProbabilityActual

If 6 boys and 3 girls are to be seated on chairs for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

Options

  1. A13 16
  2. B51 16
  3. C49 16
  4. D19 16

Correct answer

A. 13 16

Step-by-step solution

Total arrangements of 9 distinct individuals are 9! = 362880 . For favorable arrangements , two girls occupy the end seats: P(3,2) = 3 2 = 6 ways. The remaining girl must be placed in a non-adjacent middle seat: 5 valid positions. The 6 boys then arrange in the remaining seats: 6! = 720 ways. Thus, favorable outcomes are 6 5 720 = 21600 . The probability is 21600 362880 = 5 84 .

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