### Select your language

Suggested languages for you:

Americas

Europe

Problem 1061

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

Expert verified
There are 24 permutations of three elements taken from a set of four elements $$\{a, b, c, d\}$$.
See the step by step solution

## Unlock all solutions

Get unlimited access to millions of textbook solutions with Vaia Premium

Over 22 million students worldwide already upgrade their learning with Vaia!

## 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 $$\{a, b, c, d\}$$.

We value your feedback to improve our textbook solutions.

## Access millions of textbook solutions in one place

• Access over 3 million high quality textbook solutions
• Access our popular flashcard, quiz, mock-exam and notes features
• Access our smart AI features to upgrade your learning

## Join over 22 million students in learning with our Vaia App

The first learning app that truly has everything you need to ace your exams in one place.

• Flashcards & Quizzes
• AI Study Assistant
• Smart Note-Taking
• Mock-Exams
• Study Planner