3 Grade Math:

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。

3Grade Math,PermutationCombination,Factorial