Combinatorial Kingdom

Probability Level 3

There are 3 gates numbered 1, 2 and 3 to enter a kingdom. In how many ways can 100 visitors get inside the kingdom?

Details and Assumptions:

Assume that at a time only one person can get inside the kingdom through one of the gates.

Solve more problems like this in my set Combinatorics

102 ! 2 ! \frac{102!}{2!} 102 ! 4 ! \frac{102!}{4!} 102 ! 5 ! \frac{102!}{5!} 102 ! 3 ! \frac{102!}{3!}

Nikhil Ramakrishnan by Nikhil Ramakrishnan , 22, India

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1 solution

Geoff Pilling
Jan 5, 2019

You can use a stars and bars approach where the 🌟 s are the people and the bars are the dividers between the gates. There are ( 102 2 ) \binom{102}{2} or 102 ! 2 ! \frac{102!}{2!} possible ways.

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