Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Can any one help me in proving the following equality:
$$n^n= \sum_{i=1}^n {n \choose i}* i^{i-1}* (n-i)^{n-i}$$$$n^n= \sum_{i=1}^n {n \choose i}\cdot i^{i-1}\cdot (n-i)^{n-i}$$
I tried some different ideas but none of them worked!
$$n^n= \sum_{i=1}^n {n \choose i}* i^{i-1}* (n-i)^{n-i}$$
$$n^n= \sum_{i=1}^n {n \choose i}\cdot i^{i-1}\cdot (n-i)^{n-i}$$
