Thread: Problem involving factorials and "choosing"

1. Problem involving factorials and "choosing"

Q: Using the identity nC{r-1} + nCr = {n+1}Cr. Find a value of n which satisfies the equation:
4C{n-1} + 4Cn = 5.

My attempted solution:

4C{n-1} + 4Cn = 5
5Cn = 5 (by the identity given)
{5!}/{n!(5-n)!}=5
4! = n!(5-n)!

Then i'm stuck - I can get the answer by trial and error using the fact that n is obviously between 0 and 4 and also by comparing with Pascal's triangle at the second line of work but I'm convinced that there must be a way by carrying on with the algebra.

Thanks in advance for any help and apologies for not using LATEX i did try but failed badly.

2. Originally Posted by MrT83
Q: Using the identity ${^nC_{r-1}} + {^nC_r} = {^{n+1}C_r$. Find a value of n which satisfies the equation:
${^4C_{n-1}} + {^4C_n} = 5.$

My attempted solution:

${^4C_{n-1}} + {^4C_n} = 5$
${^5C_n} = 5$ (by the identity given)
${5!}/{n!(5-n)!}=5$
$4! = n!(5-n)!$

Then i'm stuck - I can get the answer by trial and error using the fact that n is obviously between 0 and 4 and also by comparing with Pascal's triangle at the second line of work but I'm convinced that there must be a way by carrying on with the algebra.

Thanks in advance for any help and apologies for not using LATEX i did try but failed badly.
I think that your method is as good as any. It involves a little bit of trial and error at the end, but I think that is unavoidable here.

To see the LaTeX code, hover the cursor over the formulas. Each formula needs to be wrapped in  tags.

3. Originally Posted by Opalg
To see the LaTeX code, hover the cursor over the formulas. Each formula needs to be wrapped in  tags.
Thanks! I think the problem was that I was wrapping with [tex]