Given $\displaystyle N$ i.i.d. random variables $\displaystyle X_1, X_2, ... X_N$ with distribution $\displaystyle N(0, \sigma)$

Question 1: What is the probability that there exists a set $\displaystyle A$ of the $\displaystyle X_is$ such that 1. $\displaystyle |A|=T$; 2. $\displaystyle |X_i - X_j| < w$ for all $\displaystyle X_i, X_j \in A$ and some real $\displaystyle w$.

Question 2: Let $\displaystyle B$ be the set of all such $\displaystyle A$s from Question 1, and define $\displaystyle A_{min} \in B$ such that $\displaystyle \max A_{min} < \max A_j$ for all $\displaystyle A_j \in B , A_j \neq A_{min}$. What's the probability that $\displaystyle \max A_{min} = r$ for some real number r.