2021 Combo Div 2 P4
Source:
March 2, 2021
combinatorics
Problem Statement
Vijay has a stash of different size stones: in particular, he has types of stones, with sizes from through , and he has stones of size .Vijay starts randomly (and without replacement) taking out stones from his stash and laying them out in a line. Vijay notices that the first stone of size comes before the first stone of size , the first stone of size is before the first stone of size , and so on. What is the probability of this happening?Express your answer in terms of only basic arithmetic operations (division, exponentiation, etc.) and the factorial function.Proposed by Misha Ivkov