CA Foundation · Quantitative Aptitude · Permutations and Combinations
A hospital in Nagpur has 10 doctors. A panel of 4 doctors is to be formed. In how many ways can the panel be formed if a particular senior doctor, Dr. Kulkarni, must always be on the panel?
The answer is 84. With Dr. Kulkarni fixed on the panel, the remaining 3 places are filled from the other 9 doctors, giving 9C3 = 84 ways. Choosing from all 10 would ignore the condition.
- A84Correct
- B120
- C210
- D126
Explanation
Dr. Kulkarni is fixed on the panel, so the other 3 members are chosen from the remaining 9 doctors: 9C3 = 84. Option 210 is 10C4, which ignores the condition. Option 120 is 10C3, which wrongly reduces only the panel size and not the pool.
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