In how many ways can one or more of $101$ letters be posted in $101$ letter boxes? 
In how many ways can one or more of $101$ letters be posted in $101$ 
  letter boxes?
$\quad\quad\quad\quad\quad1)10100 \quad\quad  2) 101^{100} \quad\quad 
  3) 100^{101} \quad\quad   4) 101(101^{101} - 1)/100$

I am not sure where I am going wrong in interpreting this problem but the obvious thing that came to my mind is to assume letters and letter boxes all distinct and apply mutual inclusion-exclusion but from the answer options that doesn't seems not be the correct approach for this one.where exactly I am going wrong?

Hint:  It appears you are considering all the letters and all the boxes to be distinct, but you post letters in a given order.  I can't get any of the answers to work any other way.  Then one letter can be posted to one of $101$ boxes in $101$ ways, two letters can be posted in $101^2$ ways (each letter is independent of the other), and so on.  Summing the geometric series gives what?
