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?