Permutations and Combinations - Anagrams (Condition) | Don't Memorise | GMAT/CAT/Bank PO/SSC CGL

TL;DR

Find the number of anagrams of the word "football" where the vowels are always together.

Transcript

here's a tricky problem in how many different ways can the letters of the word football be arranged such that all the vowels are always together we are talking about the word football here indirectly we have been asked for the number of anagrams we can form using the word football anagram is the word formed by simply rearranging the letters of anot... Read More

Key Insights

• ❓ The problem involves calculating anagrams with a condition of vowels being together.
• ❓ By treating the vowels as one element, the calculation becomes simpler.
• #️⃣ Factorial calculations are used to determine the number of anagrams.

Questions & Answers

Q: How can we calculate the number of anagrams for the word "football" with vowels together?

To calculate the number of anagrams, we first consider the distinct elements in the word "football" and calculate their factorial. Then, we divide by the factorial of the repeated elements.

Q: What is the reasoning behind considering the vowels as one element?

By considering the vowels as one element, we simplify the problem and treat them as a single entity. This helps in calculating the number of anagrams more effectively.

Q: How do we calculate the factorial of the distinct elements and the repeated elements?

To calculate the factorial, we multiply the numbers from 1 to the total number of elements or repeated elements, respectively. For repeated elements, we divide the factorial by the factorial of the number of repeated letters.

Q: Can you provide an example calculation for finding the number of anagrams?

For the word "football", we have six distinct elements and one element with two repeated letters. Therefore, we calculate (6!/2!) * (3!/2!) = 1080 ways to arrange the letters.

Summary & Key Takeaways

• The problem asks for the number of anagrams that can be formed using the word "football" with the condition that all vowels should be together.

• The approach is to consider the vowels as one element and count the distinct elements in the word.

• The number of anagrams is calculated by dividing the factorial of the total number of elements by the factorial of the repeated elements.