## Math Problem Statement

Tired of being CIS 1600 TAs, Kevin, Daniel, Sophia, Suzzy, and Olivia train for the new 5x1600m race in the 2028 Summer Olympics. However, they each want to be the first person to run, so they establish a procedure to determine the order of the competitors. Their coach, Dilini, has them line up in alphabetical order and tells them the following: the first two people must flip a coin to decide who gets to be the first person in the relay. The winner of the coin flip is assigned to the first spot in the relay, while the loser must stay to play the next person in line. The person who wins the next flip gets to run second, while the loser must again stay to play the next person in line. This process continues until there is only 1 TA left, who is the anchor. Basically, the winner stays, the loser continues. How many ways can the five TAs run?

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Combinatorics

Probability

Permutations

### Formulas

Binomial coefficient

Counting arrangements

### Theorems

Binomial theorem

Principle of Inclusion-Exclusion

### Suitable Grade Level

Grades 10-12

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