Derangements
Imagine you distribute 10 Books numbered from 1 to 10 to Students 1,2,…,10. How many ways are there to redistribute the books in such a way that nobody receives the …
Course: Combinatorics: Strategies and Methods for Counting
Sharings into nonempty sets
We learn here how to count the number of distributions of different objects into distinguishable boxes in such a way that no box remains empty. For instance, assume a hostel …
Uniform probability
What is the probability to win at the lottery? Or to write your name if you choose randomly one by one as many letters as your name needs? Carlo will …
The inclusion/exclusion principle: counting intersections
How about if we want to count the number of elements of the intersection of a finite number of sets? Well, there’s a nice formula that comes directly from the …
Let’s count. Occupancy problems with sequences
Do your best in trying to solve the following problem. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Characteristic OGF and EGF
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Occupancy problems with compositions
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Sum and product of formal power series
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Compositions with constraints
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Sequences with occupancy
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Collections
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
Let’s count. Compositions
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
The course structure
Every activity contains some steps where Alberto or Carlo explain the main topics. This will be followed by one or two Let’s count steps, where you’ll find some exercises and …
Let’s count. Counting sequences
Do your best in trying to solve the following problems. It is normal that this step will take some time, we recommend to perseverate and wait before looking at the …
These articles are from the online course:
Combinatorics: Strategies and Methods for Counting