5here are 10 fingers( 5 on each hands), 

> 
> # of ways to hold up exactly 3 fingers?  
> 
>  # of ways to hold up exactly 3 fingers on each hand?  
> 
>  # of ways to hold some finger up, when i'm holding up at least one in each hand?
> 
> 
> 

I believe the answer for the first is $\binom{10}3$ and for second one it would
be $\binom{5}3+\binom{5}3$. Am I right on this part?

I believe the 3rd one holds same logic. Can someone explain this with
thorough explanation?