Formula nCr to power of p [closed]
Is there a formula to convert N choose K to X to the power of P, where X can be 2 or 10.
(n k) == x^p
p = ?
Solution 1:
Using the definition $$\begin{pmatrix} n \\ k \end{pmatrix} = \frac{n!}{k! (n-k)!}.$$ If we have $$ x^p = \begin{pmatrix} n \\ k \end{pmatrix}$$ (where $x \ne 1$) then this implies $$p = \frac{1}{\log(x)}\left(\sum_{i=n-k+1}^n \log(i) - \sum_{i=1}^k \log(i)\right)$$.