Need help solving a combination for n

1. Nov 27, 2004

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?

2. Nov 27, 2004

Gokul43201

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

3. Nov 27, 2004

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?

4. Nov 27, 2004

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

5. Nov 27, 2004

Gokul43201

Staff Emeritus
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.

6. Nov 27, 2004

ms. confused

Thank you for the help!

7. Nov 28, 2004

prasanna

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

8. Nov 28, 2004

nolachrymose

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

9. Nov 29, 2004

prasanna

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