How to solve $$\sum_{r=0}^{2022} (-1)^r. {2022\choose r}(2022-r)^{2022}$$
My try:
I am able to solve questions like $$\sum_{r=0}^{2022} (-1)^r. {2022\choose r}(2022-r)$$ by expanding it into two summations and solving both separately. But in this question $(2022-r)$ is also raised to power. When I am trying to expand $(2022-r)^{2022}$ using binomial expansion, I am not getting any solvable results.
I even tried replacing $r$ with $2022-r$ $$\sum_{r=0}^{2022} (-1)^{-r}. {2022\choose r}(r)^{2022}$$ But I dont know how to solve this also
Can anyone please provide some hint for alternative approaches or how to proceed with above mentioned approach. Thanks!
