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10 Aug 2016, 09:50
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Sixteen jobs are vacant; how many different batches of men can be chosen out of twenty candidates ? How often may any particular candidate be selected ?
Answer is 20C16 and
For second Answer is 19C15, How??
Can anyone, please explain how to solve this question.
Thanks in advance.
Answer is 20C16 and
For second Answer is 19C15, How??
Can anyone, please explain how to solve this question.
Thanks in advance.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
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10 Aug 2016, 17:53
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Hi Piyushgmatt,
What is the source of this question? If it's a GMAT question, then it should include 5 answer choices. In many cases, the answer choices provide a clue as to how you might go about solving the prompt. Without having those answers though, we're forced to approach this prompt arithmetically (which is sometimes not the fastest way to get to the correct answer). It should also be posted in the Quant Forums.
The prompt doesn't specify whether the 16 jobs are different jobs or the same job, but the 'intent' of the question is that the sixteen men are interchangeable (any of them can do any job and there's nothing differentiating one job from any of the others). In that way, we have a Combination question, so we can use the Combination Formula:
N!/K!(N-K)! where N is the total number of people and K is the size of the sub-group. We're choosing 16 men from a group of 20...
20!/16!(4!) = (20)(19)(18)(17)/(4)(3)(2)(1)
The second part of the question asks how many times any individual person could be selected under these conditions. If we "lock in" one of the spots for "Person X", then there are 15 other spots remaining for the other 19 men. The same Combination Formula is used, but now we're using 19 and 15 for N and K...
19!/15!(4!)
GMAT assassins aren't born, they're made,
Rich
What is the source of this question? If it's a GMAT question, then it should include 5 answer choices. In many cases, the answer choices provide a clue as to how you might go about solving the prompt. Without having those answers though, we're forced to approach this prompt arithmetically (which is sometimes not the fastest way to get to the correct answer). It should also be posted in the Quant Forums.
The prompt doesn't specify whether the 16 jobs are different jobs or the same job, but the 'intent' of the question is that the sixteen men are interchangeable (any of them can do any job and there's nothing differentiating one job from any of the others). In that way, we have a Combination question, so we can use the Combination Formula:
N!/K!(N-K)! where N is the total number of people and K is the size of the sub-group. We're choosing 16 men from a group of 20...
20!/16!(4!) = (20)(19)(18)(17)/(4)(3)(2)(1)
The second part of the question asks how many times any individual person could be selected under these conditions. If we "lock in" one of the spots for "Person X", then there are 15 other spots remaining for the other 19 men. The same Combination Formula is used, but now we're using 19 and 15 for N and K...
19!/15!(4!)
GMAT assassins aren't born, they're made,
Rich
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
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