Problem 1059 Calculate the number of permutat... [FREE SOLUTION]

Chapter 33: 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.

Step by step solution

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.

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.

Apply the Permutation Formula

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

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

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

Short Answer

Step by step solution

Understand Permutations and the Permutation Formula

Identify the number of items and how many at a time

Apply the Permutation Formula

Simplify and Calculate the Permutations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Decision Maths

Pure Maths

Discrete Mathematics

Geometry

Calculus

Study anywhere. Anytime. Across all devices.