Factorials and Permutations by 垃圾桶

📌 Key Concepts:

taot0803 — 2025-05-20 03:26:45 UTC

🔹 Factorial (n!)

🔹 Permutations

Definition: The number of arrangements of objects where order matters.
Formula (no repetition):
P(n,r)=n!/(n−r)!

Where:
- n: total items
- r: number of items being chosen/arranged
With Repetition:
Total permutations=n!/n1!×n2!×⋯×nk!
Use this when there are repeated elements (like letters in "LEVEL").

taot0803 — 2025-05-20 03:27:05 UTC

Use permutations when the order matters (e.g., rankings, passwords).
Use factorials to count total arrangements.
Repetition reduces total permutations — divide by factorials of repeated elements!

taot0803 — 2025-05-20 03:27:55 UTC

Q: How many ways can the letters in the word "MATH" be arranged?

All 4 letters are unique:

4!=4×3×2×1=24

taot0803 — 2025-05-20 03:28:48 UTC

Q: How many distinct arrangements are there for the word "PEPPER"?

A:
There are 6 letters, with repeated letters:

6!/3!×2!×1!=720/6×2=60