2
A committee of 4 people is to be appointed from 3 officers of the production department, 4 officers of the purchase
department, 2 officers of the sales department and 1 chartered accountant. The probability that the chartered accountant
must be in the committee is
EXPLANATION
Numerical Methods
- Probability with Combinations:
- Composition of eligible officers:
- Production department: 3
- Purchase department: 4
- Sales department: 2
- Chartered Accountant (CA): 1
- Total pool size: $N = 3 + 4 + 2 + 1 = 10$ individuals
- Committee size: $k = 4$ individuals
- Direct Symmetry Method:
- Since each of the 10 individuals has an equal chance of being chosen in a committee of 4, the probability that any specific individual (the CA) is included is simply:
- Combinatorial Verification:
- Total number of possible committees: $\binom{10}{4} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210$
- Favorable committees (including the 1 CA, remaining 3 chosen from the other 9): $\binom{1}{1} \times \binom{9}{3} = 1 \times \frac{9 \times 8 \times 7}{3 \times 2 \times 1} = 84$
- Probability: $P = \frac{84}{210} = \frac{2}{5}$
- Conclusion: The probability is 2/5 (Option 4).
Correct option: (4) 215
Explanation not matching this question?
क्या व्याख्या इस प्रश्न से मेल नहीं खा रही?
Report
Want to practice this paper in exam conditions?
क्या आप परीक्षा जैसे माहौल में अभ्यास करना चाहते हैं?
Test yourself in 5-question batch format with timer and hidden answers.
5-प्रश्नों के बैच फॉर्मैट, टाइमर और छिपे उत्तरों के साथ खुद को परखें।
Start Practice Mode →
प्रैक्टिस टेस्ट मोड शुरू करें →