An arrangement of objects where their order matters. Example: 1-2-3 and 3-2-1 are different permutations of the digits 1, 2, and 3.
Multiply the remaining choices at each step to get the total.
How many ways to line up \(n\) different books.
Possible finishing orders for \(n\) runners, each place different.
Use multiplication rule to count 3-digit codes.
How many different 3-digit lock codes can be formed?
Multiplication rule: total outcomes = product of choices for each position.
How many 4-digit numbers have distinct digits?
9 choices: digits 1–9. Zero can’t lead.
9 remaining digits: 0–9 except the thousand digit.
8 digits left.
7 digits left.
\(9\times9\times8\times7 = 4\,536\) distinct 4-digit numbers.
Outcome: You can now count arrangements when digits must be different.
Hands-on practice: Drag each coloured ball into the three spots, use each ball once, then read the permutation count.
1st
2nd
3rd
Try all possibilities, then multiply choices!
Order matters: 12 and 21 are different.
All different items: count with \(n!\).
Fixed spots? Multiply the remaining choices one at a time.
No repeats allowed: available choices drop each step.
Prepare for tougher problems: try counting circular arrangements.
Thank You!
You now recall the core facts and are ready for harder problems.