What I have is

\( E[x_i]=\sum_{j=1}^{N}X_j Pr(x_i=X_j) \)

Then

\( Pr(x_i=X_j) = 1/N \)

This is the bit I can't understand, how does that probability evaluate to that value.

I know the denominator is how many ways you can choose n out N. I think that the numerator should be how many ways you can choose (n-1) out of (N-1). But I seem to have an extra n.

Any advice ?