Unleashing the Power of Three-Letter Words: SUCCESS Permutations Guide

Table of Contents

1. Introduction
2. How Many Three-Letter Words Can Be Made?
3. Case 1: Single Letters, No Repetition
4. Case 2: One Double Letter
5. Case 3: Triple Letter
6. Combining All Cases
7. Conclusion
8. Pros and Cons
9. Frequently Asked Questions (FAQ)

How Many Three-Letter Words Can Be Made?

Have You ever wondered how many three-letter words can be made from a given set of letters? In this article, we will explore the concept of permutations and combinations to answer this fascinating question. We will use the word "SUCCESS" as an example and go through different cases to find the possible combinations of three-letter words.

Case 1: Single Letters, No Repetition

Let's start with the simplest case, where we consider only single letters without repetition. In the word "SUCCESS," we have seven letters: S, U, C, C, E, S, and S. However, since We Are looking for three-letter words, we need to select three letters from these seven. So, how many ways can we do that?

In this case, there are no repeated letters, so we have four distinct options to choose from. We can select any three out of these four letters, resulting in a total of 4P3 (permutations of 4 selecting 3) possible three-letter words. The answer for case 1 is 4P3, which equals 24.

Case 2: One Double Letter

Now, let's move on to the next case, where we have one double letter. In the word "SUCCESS," we have two "S" letters that can be repeated. We need to consider all possible combinations with the double letter.

In this case, we have three spaces to fill with two "C" letters. The number of ways to do that is 3P2 (permutations of 3 selecting 2), which equals 6. However, since the "C" letters are repeated, we need to divide by 2 factorial (2!) to avoid counting duplicate combinations. So, for the "C" letters, we have 6 divided by 2 factorial, resulting in 3 combinations.

Similarly, we can have the double letter "S" with either "U" or "E." So, in total, for case 2, we have 3 combinations with the "C" letters and 3 combinations with the "S" letters. Thus, the answer for case 2 is 3 multiplied by 2, which equals 6.

Case 3: Triple Letter

Next, let's consider the case where we have a triple letter. In the word "SUCCESS," we cannot have two double letters as we are limited to three positions. Therefore, the only possibility here is a triple letter combination.

In this case, we have one triple letter combination, which means there is only one way to arrange the three repeated letters. So, the answer for case 3 is 1.

Combining All Cases

To get the final answer, we need to combine all the cases. We add up the results from each case: 4P3 (24) from case 1, 3 combinations from case 2, and 1 combination from case 3.

Final Answer: 4P3 + 3 + 1 = 43

Therefore, there are 43 different ways to make three-letter words from the letters in the word "SUCCESS."

Conclusion

In conclusion, with the help of permutations and combinations, we have determined that there are 43 different three-letter words that can be made from the letters in the word "SUCCESS." By understanding the various cases and their combinations, we can solve similar questions and explore the fascinating world of word formations.

Pros and Cons

Pros:

• Provides a systematic approach to solve word formation problems
• Helps in understanding permutations and combinations
• Allows for exploring different cases and combinations

Cons:

• Limited to three-letter words and a specific set of letters

Frequently Asked Questions (FAQ)

Q: Can this method be applied to any word? A: Yes, the method can be applied to any word by following the same principles of permutations and combinations.

Q: What if I want to make longer words? A: For longer words, the same principles can be applied by adjusting the number of spaces and the available letters accordingly.

Q: Are there any shortcuts for solving such problems? A: Yes, there are techniques like factorial notation and combination formulas that can simplify the calculations.

Q: Can repetition be allowed in word formation? A: Yes, repetition can be allowed depending on the requirements of the problem or the given word.

Q: How does understanding permutations and combinations help in other areas? A: Permutations and combinations have applications in various fields, including mathematics, statistics, computer science, and probability theory.