Solving nC3 = 10 for n

[ms. confused]

Need help solving a combination for "n"

I've been unable to solve the following combination for "n":

nC3 =10

I got this equation : n³ - 3n² + 2n -30 = 0

But I can't find a common factor of 30 that can be plugged into the equation to equal zero. Am I solving this incorrectly perhaps? Should I be doing something different?

 

[Gokul43201]

You mistake is with the 30. How did you get that ?

 

[ms. confused]

I ended up with n³ - 3n² + 2n / 3! = 10 so I just multiplied the 3 by the 10 to get rid of the denominator. Come to think of it 3!=6 so maybe it should be 60 instead right?

 

[prasanna]

Yeah perfectly right
what you get is

n^3 - 3n^2 + 2n - 60 = 0

Solving for n
n = 5 or -1

neglecting -1

The solution is n=5

5C3 = 10

 

[Gokul43201]

Come to think of it 3!=6 so maybe it should be 60 instead right?

That's right.

Prasanna, the policy here is that we do not solve the problem for the poster, but give suggestions or point out errors. That way, the poster will actually learn how to go about problem solving.

 

[ms. confused]

Thank you for the help!

 

[prasanna]

Prasanna, the policy here is that we do not solve the problem for the poster, but give suggestions or point out errors. That way, the poster will actually learn how to go about problem solving.

Oops! Sorry I did not know that!
I will take care hereafter!

 

[nolachrymose]

Yeah perfectly right
what you get is

n^3 - 3n^2 + 2n - 60 = 0

Solving for n
n = 5 or -1

Are you sure -1 is a solution? If you plug the value into the original cubic, you get -66, not 0.

 

[prasanna]

Yeah right
n = -1 is indeed wrong
n = -1 + sqrt(11)i
or
n = -1 - sqrt(11)i