## Variation of rencontre/monmort's problem

Suppose a deck of size 2n has each number 1, 2, ..., n appearing twice. Cards are drawn in succession for this deck after it has been randomly shuffled. Let E_i = {card with label i is drawn on draw i} for 1 <= i <= n.

Let $E = \bigcup_{i=1}^{n}\ E_i$.
a) Give an expression for P(E)
b) Determine the limit of of P(union of all E_i, i=1 to n.) as n approaches infinity.
I know you're suppose to use the inclusion/exclusion principle here, but I'm not sure how and why. I think I understand it if there were only n cards withs cards from 1 to n, but the 2n deck size and the fact that there are 2 cards of each number confuses me.