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Questions tagged [combinatorics]

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8 votes
3 answers

Simple combinatorics problems using division

I would like to introduce counting principles associated with each of the 4 basic operations (addition, subtraction, multiplication, and division) before introducing permutations and combinations in ...
Steven Gubkin's user avatar
4 votes
2 answers

What are some decent apps for Hasse diagrams?

What options are out there for software that supports interactively constructing, editing, and manipulating Hasse diagrams? Their semantics is significantly constrained, so garden-variety Let’s-draw-...
Paul Tanenbaum's user avatar
2 votes
4 answers

How can 17 y.o. high school students intuit that P(n, r) stops at $n - (r - 1)$, not $n - r$?

Every year, some 17 y.o. student makes the mistake of stopping $P(n, r)$ at $\color{darkorange}{(n - r)}$, rather than $\color{forestgreen}{(n - (r - 1))}$. Because they are in their last year of high ...
user avatar
2 votes
1 answer

Partitioning objects in combinatorics

When you come to explain dividing given n number of objects into k number of groups, is it good to describe the cases involved using an example to cover as many cases as possible in order to give ...
Janaka Rodrigo's user avatar
1 vote
2 answers

What books teach the formula for the # of k-permutations of n objects, with x types, and $r_1,⋯,r_x$ = the number of each type of object?

Some of my 16 year old students hanker after the formula for the # of k-permutations of n objects, with x types, where $r_1, ⋯, r_x$ = the number of each type of object. This is more generalized than ...
user avatar
-1 votes
1 answer

Counting principles in combinatorics

How we have to start describing counting principles in combinatorics,what we need to apply first, addition principle or product principle ? I have seen many starts with product principle rather than ...
Janaka Rodrigo's user avatar