$\sigma$ is a permutation of $\mathbb{N}$,then the sum $\sum\sigma(n)/n^2$ ,$N<n<4N$

Question

The options are :

(a)$\sigma$ is only an injective function then also the sum is convergent

(b) the sum is bounded above

(c) the sum is bounded below

(d) has 0.125 as a lower bound

Now I think options (c) is correct as it will be bounded by 0.Next I think is that the (d) is not true because if I take $N=10,00,000$ then the sum has to be very large to get to $0.125$.Since the sum is finite I think (b) is true.This has been my attempt.

Also what I wanted to ask is there a general way to find all the permutations on $\mathbb{N}$