Chapter 33: Chapter 33

Problem 1061

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Determine the number of permutations of three elements taken from a set of four elements \(\\{a, b, c, d\\}\).

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There are 24 permutations of three elements taken from a set of four elements \(\{a, b, c, d\}\).

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TABLE OF CONTENTS

Step 1: Identify the values of n and k

In this exercise, we have a set of four elements and want to find the number of permutations of three elements taken from the set. This means n=4 (the number of elements in the set) and k=3 (the number of elements we want to choose from the set).

Step 2: Use the permutation formula

We will now apply the formula for permutations, which states that the permutations of k elements taken from a set of n elements is given by \(P(n, k) = \frac{n!}{(n-k)!}\). In this problem, we are given n=4 and k=3, so we can substitute those values into the formula: \[P(4,3) = \frac{4!}{(4-3)!}\]

Step 3: Calculate the factorials

Now, we need to calculate the factorials of the numbers in the formula: \[4! = 4 \times 3 \times 2 \times 1 = 24\] \((4-3)! = 1! = 1\)

Step 4: Compute the final result

With the factorials calculated, substitute those values back into the formula and compute the result: \[P(4,3) = \frac{24}{1} = 24\] Hence, there are 24 permutations of three elements taken from a set of four elements \(\{a, b, c, d\}\).

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Chapter 33: Chapter 33

Determine the number of permutations of three elements taken from a set of four elements \(\\{a, b, c, d\\}\).

Short Answer

Step by step solution

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Step 1: Identify the values of n and k

Step 2: Use the permutation formula

Step 3: Calculate the factorials

Step 4: Compute the final result

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