There are n sticks each of different heights. There are n vacant slots arranged along a line and numbered from 1 to n as we move from left to right. The sticks are placed into the slots according to a uniformly random permutation. A stick placed at i th slot is said to be a dominating stick if its height is largest among all sticks placed in slots 1 to i-1. Find the probability that ith slot contains a dominating stick.
