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Permutations

A permutation is an arrangement of objects where order matters, represented by factorial notation (n!). The number of permutations of n distinct objects is n!, while for r objects chosen from n, the formula is nPr = n! / (n - r)!. Permutations are applicable when order is significant, such as in arranging letters, numbers, or positions.

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19 views2 pages

Permutations

A permutation is an arrangement of objects where order matters, represented by factorial notation (n!). The number of permutations of n distinct objects is n!, while for r objects chosen from n, the formula is nPr = n! / (n - r)!. Permutations are applicable when order is significant, such as in arranging letters, numbers, or positions.

Uploaded by

jerwinmigue22
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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📘 Concept Notes: Permutations

🔍 What is a Permutation?
A permutation is an arrangement of objects in a specific order.

●​ ATOrder matters in permutations.​

●​ RMUT

🧠 Key Concepts
✅ 1. Factorial Notation (!)
●​ Represented as n! (read as “n factorial”).​

●​ n! = n × (n−1) × (n−2) × ... × 1​

●​ Example:​
5! = 5 × 4 × 3 × 2 × 1 = 120​

✅ 2. Permutations of n Distinct Objects


●​ If all objects are different, the number of permutations of n objects is:​
P = n!​

Example:

●​ Arranging 4 books on a shelf:​


P = 4! = 24 ways​

✅ 3. Permutations of r Objects Chosen from n (nPr)


●​ Formula:​
nPr = n! / (n - r)!​

Example:
●​ Choosing and arranging 3 students out of 5:​
5P3 = 5! / (5−3)! = 5 × 4 × 3 = 60 ways​

✅ 4. Permutations with Repeated Objects


●​ If some objects are repeated, divide by the factorials of the repeated ones:​
P = n! / (p1! × p2! × ... × pk!)​

Example:

●​ “BALLOON” has 7 letters with 2 L’s and 2 O’s:​


P = 7! / (2! × 2!) = 5040 / 4 = 1260 unique arrangements​

💡 When to Use Permutations


✔️
●​ Use permutations when order matters:​

✔️
Positions (1st, 2nd, 3rd)​

✔️
Arranging letters, numbers, people​

✔️
Lock combinations​
Race results​

✍️ Practice Tip
Ask:​

👉
"Does the order matter?"​

👉
If yes: Use permutations​
If no: Use combinations

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