How to Find n Given r and nCr?

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Discussion Overview

The discussion revolves around finding the number of objects in a population (n) when given the number of objects chosen (r) and the number of combinations (nCr). The scope includes mathematical reasoning and combinatorial concepts.

Discussion Character

  • Mathematical reasoning

Main Points Raised

  • Some participants express a desire to calculate n based on given r and nCr values.
  • One participant asks for the equation for the binomial coefficient _{n}C_{r}.
  • Another participant notes that while it is feasible for reasonable values of C and r, there is no straightforward formula, emphasizing the need for factoring and the importance of C being a binomial coefficient.
  • One suggestion involves starting the search at n=r and using the relationship (n+1)Cr = nCr*(n+1)/(n+1-r) to find a solution, indicating that this method guarantees a solution if it exists.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a simple method for calculating n, and multiple approaches and viewpoints are presented without resolution.

Contextual Notes

There are limitations regarding the assumptions about the values of C and r, and the dependency on C being a binomial coefficient is noted. The discussion also highlights that not all integers can be represented as binomial coefficients.

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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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 _{n}C_{r}?
 
kindly read on combinations and permutations and be specific..
 
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.
 
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.
 

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