Problem 17 - Algebra and Trigonometry

Question

A medical researcher needs 6 people to test the effectiveness of an experimental drug. If 13 people have volunteered for the test, in how many ways can 6 people be selected?

Step-by-Step Solution

Answer

There are 1,716 ways to select 6 people from a group of 13.

Step 1: Understand the Problem

The problem is asking for the number of ways to select 6 people from a group of 13. This is a problem of combinations, where the order of selection doesn't matter.

Step 2: Apply the combination formula

To solve this problem, use the formula for combinations, which is \( C(n, r) = \frac{n!}{r!(n-r)!} \), where 'n' is the total number of options, 'r' is the number of options chosen, and '!' signifies a factorial. Plug in the provided numbers, with n=13 (total number of volunteers) and r=6 (number of people needed).

Step 3: Calculate and simplify

Calculate the factorials and divide as required by the formula. The factorial of a number is the product of all positive integers less than or equal to the number. So, 13 factorial (13!) is 13*12*11*10*9*8*7*6*5*4*3*2*1, 6 factorial (6!) is 6*5*4*3*2*1, and (13-6) factorial, which equals 7 factorial (7!) is 7*6*5*4*3*2*1. Divide the factorial of 13 by the product of the factorials of 6 and 7 to get the solution.