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Chapter 11: Problem 43

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?

Short Answer

Expert verified
The medical researcher can select 6 people out of 13 volunteers in 1,716 different ways.

Step by step solution

01

Understanding Combinations

A combination is a selection of items from a larger set where the order of selection does not matter. In this case, the larger set is the pool of volunteers (13 people), and the items to be selected are the test participants required (6 people). Consequently, the formula for counting combinations is C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to select, and '!' denotes factorial.
02

Substituting Values into the Formula

Substitute the given values into the formula: C(13, 6) = 13! / [6!(13-6)!].
03

Simplifying the Factorials

Calculate the factorials to simplify the equation: 13! equals to 6,227,020,800, 6! equals to 720, and (13-6)!, which is 7!, equals to 5,040. Substitute these values back into the formula: 6,227,020,800 / (720 * 5,040).
04

Calculate the Final Answer

Lastly, perform the division to get the final answer: 1716.

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