Permutations of repeated letters in a word

Understanding Permutations of Repeated Letters in a Word

• Permutations are ways of arranging items where order matters.
• In permutations of words, distinct arrangements of the letters in the word are considered.
• However, this becomes interesting when there are repeated letters in a word, as these can’t be distinguished in different arrangements.

Calculating Permutations of Repeated Letters

• Recall that the total number of permutations for ‘n’ distinct items is n factorial (n!).
• When a word has repeated letters, you divide the total permutations by the factorial of the repetition times.
• Mathematically, for a word with ‘n’ letters overall and ‘r’ repeated letters, the formula would be n! / r!.

Example: The Word ‘Letters’

• The word ‘letters’ has 7 distinct spots where a letter could be (7!).
• The letter ‘t’ and ‘e’ both repeats twice (2! for each) and ‘l’, ‘r’, and ‘s’ all occur once.
• So the number of distinct permutations would be calculated as 7! / (2! * 2!).

Key Points to Remember

• The order of letters in different permutations always matters.
• The letters that repeat have to be taken into account to ensure the permutations counted are distinct.
• Many problems based on permutations of repeated letters involve understanding and applying the right formula.

Practice and More Practice

• Understanding permutations of repeated letters is more about practice than complicated maths theory.
• Find a collection of words with repeated letters and try to calculate the permutations for each.
• Check against a permutations calculator or solution guide to see if you’re getting the correct answers.
• With more practice, spotting and calculating these permutations should become second nature.

Remember, understanding theoretical concepts in combination with ample problem-solving practice is the route to mastering permutations of repeated letters in a word. Keep using examples and exercises to improve your skills.