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Chapter 11: Problem 59

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
Using the combinations formula, the researcher can select 6 people for the experiment in 1,716 ways.

Step by step solution

01

Understand the Combinations Concept

This problem involves combinations, which are about choosing items from a group without taking the order into account. This means that item A followed by item B is the same as item B followed by item A.
02

Apply the Combinations Formula

The combinations formula is denoted as \( C(n, r) = \frac{n!}{r!(n-r)!} \) where \( n \) is the total number of items, and \( r \) is the number of items to choose. Here, \( n = 13 \) (the total number of volunteers), while \( r = 6 \) (the number of people needed for the experiment). So, we can use the formula to find out in how many ways the researcher can select 6 people from 13 volunteers.
03

Calculate the Combination

By substituting \( n = 13 \) and \( r = 6 \) in the combination formula, we get \( C(13, 6) = \frac{13!}{6!(13-6)!} \). '!' denotes factorial which means multiplying all whole numbers from the chosen number down to 1.

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Most popular questions from this chapter

Use the formula for the sum of the first n terms of a geometric sequence to solve Exercises \(71-76\). A pendulum swings through an arc of 16 inches. On each successive swing, the length of the arc is \(96 \%\) of the previous length. $$ \begin{array}{cccc} {16,} & {0.96(16),} & {(0.96)^{2}(16),} & {(0.96)^{3}(16)} \\ {\text { Ist }} & {2 \text { nd }} & {3 \text { rd }} & {4 \text { th }} \\ {\text { swing }} & {\text { swing }} & {\text { swing }} & {\text { swing }} \end{array} $$ After 10 swings, what is the total length of the distance the pendulum has swung?

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