Find the number of 4 letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed?

To solve the problem of finding the number of 4-letter words that can be formed from the letters of the word "ROSE," where repetition of letters is not allowed, we can proceed as follows:

1. **Identify the letters**: The word "ROSE" consists of 4 distinct letters: R, O, S, and E.

2. **Determine the number of permutations**: Since all 4 letters are distinct and we want to form a 4-letter word with no repetition allowed, we need to find the number of permutations of these 4 letters.

   The number of permutations of 4 distinct letters is given by the factorial of 4, denoted as \(4!\).

3. **Calculate \(4!\)**:
   \[
   4! = 4 \times 3 \times 2 \times 1 = 24
   \]

Thus, the number of 4-letter words that can be formed from the letters of the word "ROSE," without repetition, is **24**.

Would you like more details on permutations, or do you have any other questions?

---

**Related Questions**:
1. How many 3-letter words can be formed using the letters of the word "ROSE" without repetition?
2. What is the number of 4-letter words that can be formed if repetition of letters is allowed?
3. If the letters in "ROSE" were not distinct (e.g., "ROSS"), how would the number of permutations change?
4. What is the number of ways to arrange the letters of "ROSE" if two specific letters (e.g., R and O) must be next to each other?
5. How many different ways can you arrange the letters of "ROSE" if the word must start with an R?

**Tip**: Remember that the factorial of a number \(n\) (denoted as \(n!\)) represents the product of all positive integers up to \(n\). This is a fundamental concept in counting permutations.

Find the number of 4-letter words, with or without meaning, which can be formed out of the letters of the word ROSE, where the repetition of the letters is not allowed?

Discover how to find the number of 4-letter words that can be created from the letters of 'ROSE' without repetition. This problem involves understanding permutations and using the factorial formula. Perfect for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation