MathDB
2023 Combinatorics #1

Source:

April 17, 2023

Problem Statement

There are 800800 marbles in a bag. Each marble is colored with one of 100100 colors, and there are eight marbles of each color. Anna draws one marble at a time from the bag, without replacement, until she gets eight marbles of the same color, and then she immediately stops.
Suppose Anna has not stopped after drawing 699699 marbles. Compute the probability that she stops immediately after drawing the 700700th marble.