Calculating n given r and nCr?

  • Thread starter moonman239
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In summary, the conversation discusses the process of calculating the number of objects in a given population, based on a chosen number of objects and the total number of possible combinations. The equation for nCr is mentioned and it is noted that there is no simple formula for this calculation. It is suggested to use a simple search method to find a solution, starting at n=r and using the formula (n+1)Cr = nCr*(n+1)/(n+1-r). The importance of C being a binomial coefficient is also emphasized.
  • #1
moonman239
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I wish to calculate the number of objects in the population I'm selecting from, given that I am choosing r objects and there are nCr different combinations.
 
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  • #2
moonman239 said:
I wish to calculate the number of objects in the population I'm selecting from, given that I am choosing r objects and there are nCr different combinations.

Do you know the equation for [itex]_{n}C_{r}[/itex]?
 
  • #3
kindly read on combinations and permutations and be specific..
 
  • #4
You can do it for reasonable values of C and r but there is no simple formula- it is really a matter of factoring as you can the specific value of C. And, of course, it is important that C actually be a binomial coefficient. The great majority of integers are NOT.
 
  • #5
It can be done by a simple search starting at n=r and using (n+1)Cr = nCr*(n+1)/(n+1-r). Since the terms are increasing it is guaranteed to find a solution if it exists.
 

1. What is the formula for calculating n given r and nCr?

The formula for calculating n given r and nCr is n = nCr / r!

2. How do I find the value of nCr?

The value of nCr can be found by using the formula nCr = n! / (r! * (n-r)!), where n represents the total number of items and r represents the number of items being chosen.

3. Can I use a calculator to calculate n given r and nCr?

Yes, most scientific calculators have a function for calculating nCr, which can then be used to find the value of n.

4. What is the difference between n and r in nCr?

n represents the total number of items in a set, while r represents the number of items being chosen from that set.

5. Can I use the nCr formula for non-integer values of n and r?

No, the nCr formula is only applicable for positive integers. For non-integer values, you will need to use a different formula or approximation method.

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