C5
Ordered Selection
排列
Counting / 计数Grades G5 - G8
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Questions about arranging items in a specific order
- 2Words like 'permutation', 'arrangement', 'sequence'
- 3Selecting items where order matters (first, second, third)
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What It Really Tests
The core mathematical idea behind this structure:
When order matters, count all possible arrangements of selected items.
当顺序重要时，计算所选物品的所有可能排列。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Treating it as combination when order actually matters
- ⚠Not reducing the count as items are selected
- ⚠Forgetting to account for restrictions on certain positions
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Your First Step
How to begin thinking about problems with this structure:
Multiply decreasing choices: n choices for first, (n-1) for second, etc.
依次递减相乘：第一个n种选择，第二个(n-1)种选择，等等。
Related Structures
These structures share similar patterns or thinking approaches: