A7
Derangement
错位排列
Arrangement / 排列组合Grades G7 - G8
👀
What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1No item can be in its original position
- 2Questions about 'complete mismatch' or 'all wrong positions'
- 3Secret Santa or hat-swapping problems
🎯
What It Really Tests
The core mathematical idea behind this structure:
Count arrangements where no item appears in its original position.
计算没有任何物品在原位置的排列。
⚠️
Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Simply subtracting n from n!
- ⚠Not using inclusion-exclusion properly
- ⚠Missing some constrained cases
💡
Your First Step
How to begin thinking about problems with this structure:
Use inclusion-exclusion: total arrangements minus those with at least one fixed point.
使用容斥原理：总排列减去至少有一个固定点的排列。
Related Structures
These structures share similar patterns or thinking approaches: