A6
Arrangement with Repetition
重复排列
Arrangement / 排列组合Grades G5 - G8
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What It Looks Like
Recognition signals — when you see these, think of this structure:
- 1Arranging items where some are identical
- 2Words like 'distinct arrangements' with repeated letters or objects
- 3Questions about words with repeated letters
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What It Really Tests
The core mathematical idea behind this structure:
When some items are identical, divide by the factorial of each group of identical items.
当有相同物品时，除以每组相同物品的阶乘。
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Why Students Get Stuck
Common mistakes to watch out for:
- ⚠Not dividing by factorials of repeated items
- ⚠Miscounting the number of each type
- ⚠Forgetting some items are identical
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Your First Step
How to begin thinking about problems with this structure:
Count total arrangements, then divide by the product of factorials for each repeated item.
计算总排列数，然后除以每个重复物品的阶乘的乘积。
Related Structures
These structures share similar patterns or thinking approaches: