Understanding Permutation

🧮 Understanding Permutation

🔹 What is Permutation?

Permutation means arranging things in order. When we change the order, we get a different arrangement. That’s what we call a permutation.

Permutation = Arrangement

🔹 Example: Arranging A, B, C

We have three letters: A, B, and C. Let’s see how many ways we can arrange them.

Arrangement Number	Arrangement
1	ABC
2	ACB
3	BAC
4	BCA
5	CAB
6	CBA

✅ There are 6 different permutations.

🔹 Formula for Permutations

If we have n items and we want to arrange r of them:

P(n, r) = n! / (n - r)!

n! (n factorial) means multiplying all whole numbers from n down to 1.
Example: 3! = 3 × 2 × 1 = 6

🔹 Worked Example 1

Arrange 4 students (A, B, C, D) in a line.

P(4, 4) = 4! / (4 - 4)! = 4! / 0! = 24 / 1 = 24 ways

🔹 Worked Example 2

Arrange 3 students out of 5.

P(5, 3) = 5! / (5 - 3)! = 5 × 4 × 3 = 60 ways

No	Visual	Order	No	Visual	Order
1	🟩🟦🟥	A, B, C	31	🟨🟧🟩	D, E, A
2	🟩🟥🟦	A, C, B	32	🟨🟧🟦	D, E, B
3	🟩🟦🟨	A, B, D	33	🟨🟧🟥	D, E, C
4	🟩🟥🟨	A, C, D	34	🟨🟧🟩	D, E, A
5	🟩🟦🟧	A, B, E	35	🟨🟧🟩	D, E, A
6	🟩🟥🟧	A, C, E	36	🟨🟧🟦	D, E, B
7	🟩🟨🟦	A, D, B	37	🟧🟩🟦	E, A, B
8	🟩🟨🟥	A, D, C	38	🟧🟩🟥	E, A, C
9	🟩🟨🟧	A, D, E	39	🟧🟩🟨	E, A, D
10	🟩🟧🟦	A, E, B	40	🟧🟩🟥	E, A, C
11	🟩🟧🟥	A, E, C	41	🟧🟩🟨	E, A, D
12	🟩🟧🟨	A, E, D	42	🟧🟦🟩	E, B, A
13	🟦🟩🟥	B, A, C	43	🟧🟦🟥	E, B, C
14	🟦🟩🟨	B, A, D	44	🟧🟦🟨	E, B, D
15	🟦🟩🟧	B, A, E	45	🟧🟥🟩	E, C, A
16	🟦🟥🟩	B, C, A	46	🟧🟥🟦	E, C, B
17	🟦🟥🟨	B, C, D	47	🟧🟥🟨	E, C, D
18	🟦🟥🟧	B, C, E	48	🟧🟨🟩	E, D, A
19	🟦🟨🟩	B, D, A	49	🟧🟨🟦	E, D, B
20	🟦🟨🟥	B, D, C	50	🟧🟨🟥	E, D, C
21	🟦🟨🟧	B, D, E	51	🟧🟨🟦	E, D, B
22	🟦🟧🟩	B, E, A	52	🟧🟨🟥	E, D, C
23	🟦🟧🟥	B, E, C	53	🟧🟨🟩	E, D, A
24	🟦🟧🟨	B, E, D	54	🟧🟥🟩	E, C, A
25	🟥🟩🟦	C, A, B	55	🟧🟥🟦	E, C, B
26	🟥🟩🟨	C, A, D	56	🟧🟦🟩	E, B, A
27	🟥🟩🟧	C, A, E	57	🟧🟦🟥	E, B, C
28	🟥🟦🟩	C, B, A	58	🟧🟦🟨	E, B, D
29	🟥🟦🟨	C, B, D	59	🟧🟩🟥	E, A, C
30	🟥🟦🟧	C, B, E	60	🟧🟩🟦	E, A, B

🔹 Real-Life Examples

• Arranging students in a line.
• Creating password combinations.
• Organizing books on a shelf.
• Different seating orders in a photo.

🔹 Practice Questions

1. How many ways can you arrange 2 letters from A, B, C, D?
2. How many different 3-digit numbers can be made using 1, 2, 3, and 4 (without repetition)?

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🎯 Interactive Quiz: Test Your Understanding!

🎯 Interactive Quiz: Test Your Understanding!

1️⃣ How many permutations of the letters A, B, and C are there?

1. 4
2. 5
3. 6 ✅

Show Answer

✅ There are 6 permutations: ABC, ACB, BAC, BCA, CAB, CBA.

2️⃣ What does 4! (4 factorial) mean?

1. 4 + 3 + 2 + 1
2. 4 × 3 × 2 × 1 ✅
3. 4 ÷ 3 ÷ 2 ÷ 1

Show Answer

✅ 4! = 4 × 3 × 2 × 1 = 24

3️⃣ If n = 5 and r = 3, what is P(5,3)?

1. 10
2. 30
3. 60 ✅

Show Answer

✅ P(5,3) = 5! / (5 - 3)! = 5 × 4 × 3 = 60

4️⃣ In permutation, does the order matter?

1. Yes ✅
2. No

Show Answer

✅ Yes, order matters in permutation.