Questions tagged [combinatorics]

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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 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
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 ...
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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 ...
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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