Originally Posted by

**MrT83** Q: Using the identity $\displaystyle {^nC_{r-1}} + {^nC_r} = {^{n+1}C_r$. Find a value of n which satisfies the equation:

$\displaystyle {^4C_{n-1}} + {^4C_n} = 5.$

My attempted solution:

$\displaystyle {^4C_{n-1}} + {^4C_n} = 5$

$\displaystyle {^5C_n} = 5$ (by the identity given)

$\displaystyle {5!}/{n!(5-n)!}=5$

$\displaystyle 4! = n!(5-n)!$

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.