Question

A medical researcher needs 8 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 8 people be selected?

Answer 1

To find the number of ways to select 8 people from 13 volunteers, use the combinations formula C(n, k) = n! / (k!(n-k)!), which results in C(13, 8) = 13! / (8!5!) or 1,287 possible combinations.

Step-by-step explanation:

The question asks how many ways 8 people can be selected from a group of 13 volunteers for a medical trial. This type of problem is a classic combinatorial question, which can be solved using the concept of combinations. The formula to determine the number of combinations is given by C(n, k) = n! / (k!(n-k)!), where n is the total number of items to choose from, k is the number of items to choose, n! represents the factorial of n, and k! represents the factorial of k.

Using this formula for our case:

1. Calculate the factorial for 13, which is 13!.
2. Calculate the factorial for 8, which is 8!.
3. Subtract the number of people to select from the total number, that is 13 - 8, which equals 5.
4. Calculate the factorial for 5, which is 5!.
5. Finally, divide the factorial of 13 by the product of the factorials of 8 and 5 to find the number of combinations.

The solution can be simplified to C(13, 8) = 13! / (8!5!) which equals 1,287 possible ways to select 8 people from the group of 13 volunteers.