Start free

Mathematics · Probability

JEE Main 2025 — 4 April, Morning Shift — Question 28

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

  1. Option A:

    103182\frac{103}{182}

  2. Option B:

    1926\frac{19}{26}

  3. Option C:

    1726\frac{17}{26}

  4. Option D:

    129182\frac{129}{182}

    Correct

Answer: D

Step-by-step solution

3E,1D,8P3E, \quad 1D, \quad 8P 3E,2D,7P3E, \quad 2D, \quad 7P 4E,1D,7P4E, \quad 1D, \quad 7P 4E,2D,6P4E, \quad 2D, \quad 6P P=4C3⋅2C1⋅10C8+4C3⋅2C2⋅10C7+4C4⋅2C1⋅10C7+4C4⋅2C2⋅10C610C12P = \frac{{}^4C_3 \cdot {}^2C_1 \cdot {}^{10}C_8 + {}^4C_3 \cdot {}^2C_2 \cdot {}^{10}C_7 + {}^4C_4 \cdot {}^2C_1 \cdot {}^{10}C_7 + {}^4C_4 \cdot {}^2C_2 \cdot {}^{10}C_6}{{}^{10}C_{12}} =4⋅2⋅45+4⋅1⋅120+1⋅2⋅120+1⋅1⋅21045= \frac{4 \cdot 2 \cdot 45 + 4 \cdot 1 \cdot 120 + 1 \cdot 2 \cdot 120 + 1 \cdot 1 \cdot 210}{45} P=8⋅45+4⋅120+2⋅120+1⋅21045P = \frac{8 \cdot 45 + 4 \cdot 120 + 2 \cdot 120 + 1 \cdot 210}{45} =360+480+240+21045=129045= \frac{360 + 480 + 240 + 210}{45} = \frac{1290}{45} =129182= \frac{129}{182}

Answer key and solution verified before publishing.

Practise Probability

Start with this question, then two more from the same chapter — with a tutor that explains every step. Free.

Solve a similar one free
Exam
JEE Main 2025
Paper
4 April, Morning Shift
Subject
Mathematics
Chapter
Probability
Topic
Problems based on P & C

More Probability questions from this paper