# Combinatorics/Permutation problem?

• ArcanaNoir
In summary, there are 1728 possible seating arrangements when 4 American, 2 French, and 3 British people are to be seated in a row, with people of the same nationality sitting next to each other. This is calculated by multiplying the factorial arrangements of each nationality group.
ArcanaNoir

## Homework Statement

If 4 American, 2 French, and 3 British people are to be seated in a row, how many seating arrangements are possible when people of the same nationality must sit next to each other?

## The Attempt at a Solution

If I "glue" the people together like so: ABF then there are 3! ways to arrange them. There are 4! ways to arrange the Americans, 2! to arrange the French, and 3! ways to arrange the british. Is the answer 3!4!2!3!= 1728?

I thought you had run away!

I'm starting to think that you like these problems!

(Oh, and yes, you have it right! )

It's a miracle!

Oh, and I don't like these problems, I like passing my classes.

## 1. What is combinatorics/permutation problem?

Combinatorics/permutation problem is a branch of mathematics that deals with counting and arranging objects in a specific order. It involves finding the number of possible outcomes or arrangements when a set of objects is combined or arranged in a particular way.

## 2. What are the basic principles of combinatorics/permutation problem?

The basic principles of combinatorics/permutation problem are the multiplication principle, the addition principle, and the principle of inclusion-exclusion. The multiplication principle states that if there are m ways to do one thing and n ways to do another, then there are m x n ways to do both. The addition principle states that if there are m ways to do one thing and n ways to do another, then there are m + n ways to do either one. The principle of inclusion-exclusion states that if there are m ways to do one thing, n ways to do another, and p ways to do both, then there are m + n - p ways to do either one or both.

## 3. What is the difference between permutation and combination?

The main difference between permutation and combination is that permutation involves arranging objects in a specific order, while combination does not consider the order of the objects. Permutation is denoted by nPr, where n is the total number of objects and r is the number of objects being arranged. Combination is denoted by nCr, where n is the total number of objects and r is the number of objects being chosen.

## 4. How do I solve a combinatorics/permutation problem?

To solve a combinatorics/permutation problem, you first need to identify the type of problem it is (e.g. permutation, combination, or probability). Then, use the appropriate formula or principle to calculate the number of possible outcomes or arrangements. It is also important to carefully read the problem and understand the given information and the desired outcome. Practice and familiarity with different types of problems can also improve problem-solving skills in combinatorics/permutation.

## 5. What are some real-life applications of combinatorics/permutation problem?

Combinatorics/permutation problem has many real-life applications, such as in computer science, genetics, cryptography, and sports. In computer science, permutation is used in algorithms for searching, sorting, and data compression. In genetics, permutation is used to study the arrangement of genes on a chromosome. In cryptography, permutation is used to create secure codes and passwords. In sports, combination and permutation are used to determine the number of possible outcomes in a tournament or playoff system.

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