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.