/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 24 A woman has 5 blouses and 8 skir... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 14: Problem 24

A woman has 5 blouses and 8 skirts How many different outfits can she wear?

Short Answer

Expert verified
The woman can wear 40 different outfits.

Step by step solution

01

- Understand the Problem

Determine the total number of blouses and skirts the woman has. She owns 5 blouses and 8 skirts.
02

- Concept of Outfits

An outfit consists of one blouse and one skirt.
03

- Use Multiplication Principle

To find the total number of different outfits, multiply the number of choices for blouses by the number of choices for skirts: \[ 5 \text{ blouses} \times 8 \text{ skirts} \ = 40 \text{ different outfits} \]

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!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

multiplication principle
The multiplication principle is a fundamental concept in combinatorics. It helps us calculate the total number of outcomes for a series of choices. If there are several stages in a decision, and for each stage, there are a specific number of choices, the total number of outcomes is the product of the choices for each stage. For example, if a woman has 5 choices of blouses and 8 choices of skirts, the multiplication principle tells us the total number of outfit combinations is: \( 5 \times 8 = 40 \). This principle can be applied to various situations where you need to count the number of possible combinations.
outfits combination
In the given exercise, the concept of outfits combination involves selecting one blouse and one skirt to form a complete outfit. Each outfit is a unique combination of one item from each category. To understand this better, let's break it down:
  • One category is blouses, with 5 options.
  • The other category is skirts, with 8 options.
By combining each blouse with each skirt, we explore every possible pairing. This means we match each blouse with all the skirts, leading to a total number of combinations. Here鈥檚 the math: \(5 \text{ blouses} \times 8 \text{ skirts} = 40 \text{ different outfits}\). So, the woman can wear 40 unique outfits.
counting methods
Counting methods in combinatorics are strategies used to count the number of ways we can arrange or select items. One of the simplest and most common methods is the multiplication principle, as used in this exercise. Here are some key points:
  • **Basic Counting:** Simply list out all possible combinations (though this can get complicated with large numbers).
  • **Pigeonhole Principle:** A way to prove that if items are put into containers, at least one container must hold more than one item if there are more items than containers.
In our case, we use the multiplication principle: for selecting an outfit, we multiply the number of blouses by the number of skirts. This straightforward method ensures that we accurately determine the total number of combinations possible. Using counting methods properly allows us to manage and solve combinatorial problems efficiently.

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

A defensive football squad consists of 25 players. Of these, 10 are linemen, 10 are linebackers, and 5 are safeties. How many different teams of 5 linemen, 3 linebackers, and 3 safeties can be formed?

List all the permutations of 6 objects \(1,2,3,4,5,\) and 6 choosing 3 at a time without repetition. What is \(P(6,3) ?\)

Find the 85 th term of the sequence \(5,12,19,26, \ldots\)

Two fair dice are rolled. Determine the probability that the sum of the faces is \(12 .\)

According to the American Pet Products Manufacturers Association's \(2017-2018\) National Pet Owners Survey, there is a \(68 \%\) probability that a U.S. household owns a pet. If a U.S. household is randomly selected, what is the probability that it does not own a pet?
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.