Mathematics for Teaching Category: Combinatorics

Category: Combinatorics

Linking combination and permutation with repetition

Combinatorial problems are difficult because it’s hard to  know which formula to use in a particular problem and when you need to ‘tweak’ or totally abandon the formula. In this post I share two solutions to a problem which connects the multiplication principle, the combination formula and the formula for counting the number of permutation with…

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What makes counting problems difficult

I don’t have the numbers but I think not many will disagree with me that among those who like mathematics and find joy in the challenge of solving math problems, only very few will also like to solve combinatorial or counting problems. And if I may be allowed to push my observation a bit further,…

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Pascal’s triangle and Counting Permutations

This is the second in my series of posts in combinatorics. The first post links the Fundamental Counting Principle, Powers of 2, and the Pascal Triangle. This second post connects the Pascal’s Triangle and the formula for counting the number of permutations with identical objects. The context for connections is a puzzle about counting the…

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The Counting Principle, Pascal’s Triangle, and Powers of 2

This post shows how we can help students make connections among counting principle, the Pascal’s triangle, and powers of 2. I have tried this lesson in an in-service training program but I’ve yet to test it with students in high school. The lesson uses the strategy Teaching thru Problem Solving. A piece of knowledge is…

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