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## The factorial

The factorial of a natural (n) is the natural number [n!=ntimes (n-1)cdotstimes 2times 1] The factorial appears in several combinatorial formulas: why?

## The Multiplication Principle

We are already familiar wit sequences, sets, collections. How do we count them? We see here one of the most powerful tools in combinatorics: the Multiplication Principle. Be careful: its …

## Compositions: distribution of indistinguishable objects

How to model into mathematical terms a counting problem of distribution of indistinguishable objects? We see here the notion of composition and howit is related to that of collection.

## Bell numbers

The number of partitions that can be formed with a set containing a given number (k) of elements is the (k)-th Bell number. Let us discover how it is related …

## Some mathematical objects: sequences, sets and collections

What are the main mathematical objects that we are going to be able to count? Sequences, sets and collections will be the main characters of the MOOC.

## Sharings: distribution of distinguishable objects

How to model into mathematical terms a counting problem of distribution of distinguishable objects? We see here the notion of sharing and how it is related to that of sequence.

## Stirling numbers of the second kind

Subdividing a group of (k) students into (n) study groups produces what we call a (n)-partition of the sets of students. The number of these subdivisions is the Stirling number …

## Counting the elements of a set

Why and how difficult may it be to count the number of elements of a set?

## Meet the team

Let’s present the team. In the videos you’ll meet Alberto and Carlo , professors of mathematics at the University of Padova (Italy). You can click ‘Follow’ on the profile to …