2023 AIME I Problems/Problem 1
Problem
Solutions
Solution 1
We can reword the problem into a simpler problem to solve. The new problem is "What is the probability two men don't stand opposite of each other?" We will order the men first, since the identities of each person aren't counted. The first man can stand anywhere (
), then the second man can stand in 12 spaces out of 13, third man can stand in 10 places, so on until the fifth man stands in 6 places out of 10 possible places. ![\[\frac{14}{14}\cdot\frac{12}{13}\cdot\frac{10}{12}+\frac{8}{11}+\frac{6}{10} = \frac{48}{143}\]](http://latex.artofproblemsolving.com/1/9/8/198bd49815708bbbc4ed1dc9acc2ca402c16ac68.png)
This gives 
~chem1kall
Solution 2
Something else
See also
| 2023 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by First Question |
Followed by Problem 2 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
