Permutations of n taken r at a time

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Homework Help Overview

The discussion revolves around permutations, specifically calculating P(n,3) and P(5,r). The original poster presents two problems involving permutations and expresses uncertainty in solving a cubic equation and determining the value of r.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to solve P(n,3)=210 by forming a cubic equation but struggles with the solution. They also express confusion regarding P(5,r)=20. Some participants suggest trial and error as a method, while others inquire about solving cubic equations.

Discussion Status

Participants are exploring different methods to approach the problems, including trial and error and the use of formulas for cubic equations. There is a recognition of the relationship between n, n-1, and n-2 in the context of the first problem, and some guidance is provided regarding the second problem.

Contextual Notes

There is an implicit assumption that n must be a positive integer, and participants are considering the constraints of the permutation formulas. The original poster's uncertainty about cubic equations and the parameters for r in the second problem are noted.

PiRsq
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How can I solve these two problems?

P(n,3)=210 and P(5,r)=20

For the first one I got up to n(n-1)(n-2)=210 but I don't know how to solve a cubic equation...And the second one I have no clue. I'd appreciate some help, thanks
 
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Trial and error; there are very few possibilities. :smile:
 
Wow, its that simple? Is there any way to calculate an answer for a cubic equation?
 
There's a general formula for the cubic equation, and also for the quadric equation. On the contrary Abel showed there is no general formula to solve the quintic equation (or higher) and Galois showed why, inventing group theory in the process.
 
I see, thanks
 
You can "speed up" the trial-and-error process a little by noting that, since n, n-1, and n-2 are about the same, the problem is "close to" n3= 210. 53= 125 and 63= 216 so start trying with n-1= 6.
As for P(5,r)= 20, you know that r must be less than 5 so: P(5,0)= 1 (Of course, didn't really need to try that), P(5,1)= 5 (again "of course"), P(5,2)= 20!
 

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