### Select your language

Suggested languages for you:

Americas

Europe

Problem 1059

# Calculate the number of permutations of the letters $\mathrm{a}, \mathrm{b}, \mathrm{c}, \mathrm{d}$ taken four at a time.

### Short Answer

Expert verified
There are 24 different permutations of the letters a, b, c, and d taken four at a time.
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: Understand Permutations and the Permutation Formula

Permutations refer to arrangements of items in a specific order. The permutation formula for arranging n objects in r different ways is given by: $P(n,r) = \frac{n!}{(n-r)!}$ where n! denotes the factorial of n. The factorial function, n! = n*(n-1)*(n-2)*...*1.

## Step 2: Identify the number of items and how many at a time

In this exercise, we have 4 distinct letters (a, b, c, and d) and we want to find the permutations when selecting 4 at a time. Therefore, we have n=4 and r=4.

## Step 3: Apply the Permutation Formula

Plugging the values of n and r into the permutation formula, we get: $P(4,4) = \frac{4!}{(4-4)!}$

## Step 4: Simplify and Calculate the Permutations

Let's simplify the equation and calculate the permutations: $P(4,4) = \frac{4!}{0!}$ Here, we should note that 0! is always equal to 1. Therefore, $P(4,4) = \frac{4!}{1} = 4!$ Now calculate 4!: $4! = 4\times 3\times 2\times 1 = 24$ So, there are 24 different permutations of the letters a, b, c, and d taken four at a time.

What do you think about this solution?

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