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You’ll learn basic counting principles, and be able to explain the most frequent errors in their misuse. Ultimately, you’ll discover that combinatorics isn’t as difficult as it seems.

**What topics will you cover?**

- Convert counting problems into precise mathematical models

- Count the basic combinatorial objects like sequences and collections

- Applications on counting anagrams, derangements of a sequence (hats problem)

- Count card shuffles and understand astonishing magic tricks

- Basic probabilities (birthday problem)

- Algebraic tools that allow to solve subtle combinatorial problems

**What will you achieve?**

By the end of the course, you‘ll be able to...

- Apply the principles of combinatorics to solve the basic combinatorial problems

- Model some real life counting problems into that of counting precsie mathematical structures

- Identify the mathematical structure which lies besides a combinatorial problem: sequences, collections, sharings, compositions, partitions, derangements.

- Identify the principle to face a combinatorial problem: bijiection, multiplication, division

- Calculate the probability of an event when the sample space is composed by equiprobable elementary events

- Calculate the number of possible outcomes of an aleatory experiment

- Calculate the number of sequences of prescribed length, with or without repetitions, from a given alphabet

- Calculate the number of collections of prescribed length, with or without repetitions, from a given alphabet

- Calculate the number of sets of given cardinality

- Calculate the number of partitions of a given set in a prescribed number of subsets

- Calculate the number of permutations of a sequence without repetitions

- Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numberded boxes (possibly empty)

- Calculate the number of distributions of distinguishable/indistinguishable objects in a given number of numberded non-empty boxes

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