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To fill 12 vacancies there are 25 candidates of which 5 are from scheduled casts. If 3 of the vacancies are reserved for scheduled casts candidates while the rest are open to all. The number of ways in which the selections can be made is :
- a)5C3 * 22C9
- b)4973200
- c)27C12
- d)none
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
To fill 12 vacancies there are 25 candidates of which 5 are from sched...
Total vacancies = 12
total candidate = 25
number of scheduled caste = 5 out of 25.
reserved vacancies = 3
total ways of selection = 5C3 x 22C9
total candidate = 25
number of scheduled caste = 5 out of 25.
reserved vacancies = 3
total ways of selection = 5C3 x 22C9
Most Upvoted Answer
To fill 12 vacancies there are 25 candidates of which 5 are from sched...
Total vacancies = 12
total candidate = 25
number of scheduled caste = 5 out of 25.
reserved vacancies = 3
total ways of selection = 5C3 x 22C9
total candidate = 25
number of scheduled caste = 5 out of 25.
reserved vacancies = 3
total ways of selection = 5C3 x 22C9
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Community Answer
To fill 12 vacancies there are 25 candidates of which 5 are from sched...
Explanation:
Total Number of Ways to Fill the 12 Vacancies:
- Total number of ways to fill 12 vacancies out of 25 candidates = 25C12
Number of Ways to Fill Reserved Vacancies for Scheduled Cast Candidates:
- Number of ways to select 3 candidates from the 5 scheduled cast candidates = 5C3
- Number of ways to select 9 candidates from the remaining 20 non-scheduled cast candidates = 20C9
Calculation:
- Total number of ways = (5C3) * (20C9)
- Simplifying this expression, we get:
- (5! / 3! * 2!) * (20! / 9! * 11!)
- = 10 * 167960
- = 1679600
Therefore, the number of ways in which the selections can be made is 5C3 * 20C9, which is equal to 1679600. So, the correct answer is option 'A'.
Total Number of Ways to Fill the 12 Vacancies:
- Total number of ways to fill 12 vacancies out of 25 candidates = 25C12
Number of Ways to Fill Reserved Vacancies for Scheduled Cast Candidates:
- Number of ways to select 3 candidates from the 5 scheduled cast candidates = 5C3
- Number of ways to select 9 candidates from the remaining 20 non-scheduled cast candidates = 20C9
Calculation:
- Total number of ways = (5C3) * (20C9)
- Simplifying this expression, we get:
- (5! / 3! * 2!) * (20! / 9! * 11!)
- = 10 * 167960
- = 1679600
Therefore, the number of ways in which the selections can be made is 5C3 * 20C9, which is equal to 1679600. So, the correct answer is option 'A'.
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