Probability
Committee selection probability
nta_pyq_2025_apr
Grade 12
Question:
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:
$129 182$
$103 182$
$17 26$
$19 26$
Step-by-Step Solution
Key Concept: Compute the favourable cases for committee selection probability and divide by the total equally likely cases.
3$engineering + 1$$doctor + 8$Prof$\to$4$C_{3}$$\cdot$2$C_{1}$$\cdot$10$C_{8}$$(1) = 360$4 2 10 3$engineering + 2$$doctors + 7$Prof$\to$$C_{3}$$\cdot$$C_{2}$$\cdot$$C_{7}$= 480 4 2 10 4$engineering + 1$$doctor + 7$Prof$\to$$C_{4}$$\cdot$$C_{1}$$\cdot$$C_{7}$= 240 4 2 10 4$engineering + 2$$doctors + 6$Prof$\to$$C_{4}$$\cdot$$C_{2}$$\cdot$$C_{6}$= 210$Total = 1290$Req.$probability = 1290$16$C_{12}$= 1290$1820 = 129$182
Correct Answer: 1