Permutations with Repetition
Arrange objects when some are identical.
Key idea
Arrange objects when some are identical.
In depth
If some items are identical, divide by the factorial of each repeat count: n!/(n₁!n₂!...). Dividing removes the arrangements that only swap identical items.
Worked example
Arrangements of MISSISSIPPI: 11!/(4!4!2!) = 34,650.
Formula
Real-world uses
- Counting distinct arrangements of letters in a word such as “BANANA” or the codes for a lock
Common mistake
Forgetting to divide for each repeated letter.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Permutations with Repetition?
Arrange objects when some are identical. It is a topic at the advanced level in Discrete Math & Number Theory.
What is the formula for Permutations with Repetition?
The key formula is n!/(n₁!n₂!…).
Where is Permutations with Repetition used in real life?
Real-world examples: Counting distinct arrangements of letters in a word such as “BANANA” or the codes for a lock.
What should I learn before Permutations with Repetition?
Make sure you are comfortable with Factorials, the previous topic in Discrete Math & Number Theory.
What is a common mistake with Permutations with Repetition?
Forgetting to divide for each repeated letter.
How can I practise Permutations with Repetition?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Permutations with Repetition?
Move on to Circular Permutations next.
Related advanced topics in Discrete Math & Number Theory
- Tautologies and Contradictions – Always true or always false statements.
- Logical Equivalence – Statements with identical truth tables.
- De Morgan’s Laws – Negation swaps AND and OR.
- Converse and Contrapositive – A conditional equals its contrapositive.
- Quantifiers – “For all” and “there exists”.
- Negating Quantified Statements – Flip the quantifier and negate the predicate.