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Chapter 11: Problem 1

In Exercises 1-4, does the problem involve permutations or combinations? Explain your answer. (It is not necessary to solve the problem.) 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 problem involves combinations not permutations as the order of selection does not matter. There are \( \binom{13}{6} \) ways to choose 6 people from 13 volunteers for the test.

Step by step solution

01

Identifying the problem

Identify whether this is a combination or permutation problem. If the selection order matters, it is permutation; otherwise, it is combination. In this case, the order of selection doesn't matter. Hence, it's a combination problem.
02

Applying Combination Formula

The combination formula is \( \binom{n}{r} = \frac{n!}{r!*(n-r)!} \) , where \( n \) is the total number of individuals available, \( r \) is the number of individuals to be selected, and '!'' represents factorial. In this problem \( n = 13 \) and \( r = 6 \).
03

Calculating the combinations

Now plug \( n = 13 \) and \( r = 6 \) into the formula to calculate combinations. The number of ways 6 people can be selected out of 13 is \( \binom{13}{6} = \frac{13!}{6!*(13-6)!} \)

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