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Questions and Answers
在排列和组合中，什么时候顺序很重要？
如果从3个物品中选择2个，共有多少种组合？
如果有4个blocks排列在一行中，共有多少种排列？
什么是排列和组合的主要区别？
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从5本书中选择3本，共有多少种组合？
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Study Notes
3rd Grade Math: Permutation and Combination
Permutation
- A permutation is an arrangement of objects in a specific order.
- Example: Arrange 3 toys (A, B, C) in a row. How many different ways can they be arranged?
- ABC, ACB, BAC, BCA, CAB, CBA (6 ways)
- Formula: n! (n factorial) = n × (n-1) × (n-2) × ... × 1
- Example: 3! = 3 × 2 × 1 = 6
Combination
- A combination is a selection of objects without regard to order.
- Example: Choose 2 toys from a set of 3 toys (A, B, C). How many different combinations?
- AB, AC, BC (3 ways)
- Formula: C(n, r) = n! / (r!(n-r)!)
- Example: C(3, 2) = 3! / (2!(3-2)!) = 3 ways
Key Concepts
- Permutations are used when order matters.
- Combinations are used when order does not matter.
- Permutations involve arrangement, while combinations involve selection.
Practice Questions
- Arrange 4 blocks (R, G, B, Y) in a row. How many permutations?
- Choose 2 books from a shelf of 5 books. How many combinations?
第三级数学：排列和组合
排列
- 排列是一种特定的顺序安排对象。
- 例子：将3个玩具（A、B、C）排列在一行中。有多少种不同的排列方式？+ ABC, ACB, BAC, BCA, CAB, CBA（6种）
- 公式：n!（n的阶乘）= n × (n-1) × (n-2) ×...× 1
- 例子：3! = 3 × 2 × 1 = 6
组合
- 组合是从一组对象中选择某些对象，忽略顺序。
- 例子：从3个玩具（A、B、C）中选择2个玩具。有多少种不同的组合方式？+ AB, AC, BC（3种）
- 公式：C(n, r) = n!/ (r!(n-r)!)
- 例子：C(3, 2) = 3!/ (2!(3-2)!) = 3种
关键概念
- 排列用于顺序很重要的情况。
- 组合用于顺序无关紧要的情况。
- 排列涉及到对象的排列，而组合涉及到对象的选择。
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Description
3Grade Math,PermutationCombination,Factorial
