College

We appreciate your visit to There are 50 members in a running club A team of 3 runners is selected to attend an elite racing competition In how many ways. 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!

There are 50 members in a running club. A team of 3 runners is selected to attend an elite racing competition.

In how many ways can the 3 runners be selected?

Answer :

Final answer:

There are 117,600 ways to select a team of 3 runners from a total of 50 members in a running club using the combinations formula. The order of selection does not matter in this situation, which is why combinations are used. By applying the combination formula, we can find the answer efficiently.


Explanation:

Calculating Combinations


To find the number of ways to select a team of 3 runners from 50 members in a running club, we can use the concept of combinations. A combination is used when the order of selection does not matter. The formula for combinations is given by:


C(n, r) = n! / (r!(n - r)!)


Where:



  • n = total number of items (in this case, 50 runners)

  • r = number of items to select (in this case, 3 runners)

  • ! denotes factorial, which is the product of all positive integers up to that number.


Now, applying the values:



  2. Calculate 50!

  4. Calculate 3!

  6. Calculate (50 - 3)! = 47!


Now plug in the values to the formula:


C(50, 3) = 50! / (3! * 47!)


This simplifies to:


C(50, 3) = (50 × 49 × 48) / (3 × 2 × 1)


The calculation is:


C(50, 3) = 117600


Thus, there are a total of 117600 ways to select 3 runners from the 50 members in the running club.


Learn more about combinations here:

https://brainly.com/question/30646507


Thanks for taking the time to read There are 50 members in a running club A team of 3 runners is selected to attend an elite racing competition In how many ways. 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