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

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

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