Ball Pit Mayhem

Probability Level 4

A pile of 2 0 20 20^{20} balls distinctly labeled with the numbers 1 , 2 , … , 2 0 20 1, 2, \dots, 20^{20} are thrown randomly into a ball pit. Five friends then each take turns picking a ball from the ball pit. What is the probability that the five numbers chosen are in decreasing order based on the time they were picked?


The answer is 0.008333.

Calvin Osborne by Calvin Osborne , 18, USA

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1 solution

Nick Kent
Feb 3, 2020

The amount of balls in the pit is actually irrelevant, we only need to find the probability of the five chosen balls being in order. Since there are 5 ! 5! possible orderings for five balls, the probability is 1 5 ! = 0.00833333333 \frac{1}{5!}=\boxed{0.00833333333}

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