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JEE Main20254 Apr 2025Morning ShiftMathematicsProbabilityActual

The probability, of forming a 12 persons committee from 4 engineers, 2 doctors and 10 professors containing at least 3 engineers and at least 1 doctor, is:

Options

  1. A129 182
  2. B103 182
  3. C17 26
  4. D19 26

Correct answer

A. 129 182

Step-by-step solution

aligned & 3 engineering +1 doctor +8 Prof ^4 C ₃ ^2 C ₁ ¹⁰ C ₈ & =360 & 3 engineering +2 doctors +7 Prof ^4 C ₃ ^2 C ₂ ¹⁰ C ₇ & =480 & 4 engineering +1 doctor +7 Prof ^4 C ₄ ^2 C ₁ ¹⁰ C ₇ & =240 & 4 engineering +2 doctors +6 Prof ^4 C ₄ ^2 C ₂ ¹⁰ C ₆ & =210 aligned Total =1290 Req. probability = 1290 ¹⁶ C ₁₂ = 1290 1820 = 129 182

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