High School

We appreciate your visit to Suppose there are 6 runners in a race How many different orders can these 6 runners finish the race if no ties are allowed. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Suppose there are 6 runners in a race. How many different orders can these 6 runners finish the race if no ties are allowed?​

Answer :

Final answer:

Permutations are used to compute the number of ways 6 runners can finish a race in different orders. Using the formula of permutations P(n, r) = n! / (n-r)!, and inserting the values (6,6) leads to the conclusion that there are 720 different ways in which six runners can finish the race.

Explanation:

The subject of this question is combinatorics, a topic in mathematics. This problem can be solved using the concept of permutations - the particular ordering of things. If there are 6 runners in a race, and no ties are allowed, we need to establish the number of possible orders in which they can finish the race.

Using the formula of permutation, expressed as P(n, r) = n! / (n-r)!, in which n is the total number of options and r is the number of options chosen (where '!' signifies a factorial), we substitute our values getting P(6,6) = 6! / (6-6)!. Here, both n and r are 6 since each runner can occupy any of the 6 positions in the order of finish.

By calculating this, we recognise that 6! is the multiplication of all positive integers up to 6 (6*5*4*3*2*1=720), while (6-6)! is, basically, 0!, which equals to 1 (by definition). Thus, there are 720 different orders in which the 6 runners can finish the race, not allowing for ties.

Learn more about Permutations here:

https://brainly.com/question/23283166

#SPJ11

Thanks for taking the time to read Suppose there are 6 runners in a race How many different orders can these 6 runners finish the race if no ties are allowed. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada