Skip to 0 minutes and 3 seconds Hello, my name’s Albert. Hello, I’m Carlo. We both are mathematicians of the University of Padua, which is a very closer to Venice. Actually, we are both Venetians. Here are some problems that we are going to consider in this MOOC. How many hands of five cards can be dealt with a deck of 52? And how many have exactly three red cards? like that one, for instance. Or very famous birthday problem, which is the probability that in the class of 24 students, the least two of them share the same birthday? and there’s another one. Then tourists lift their passport at the desk. Afterwards, the clerk gives them back randomly. What is the probability that nobody receives is on passport?
Skip to 0 minutes and 56 seconds Did you know that this value is strictly related to the Euler number? True Carlo Another problem is counting the derangements of a sequence. The derangement is a complete new way of ordering the elements of a sequence. Like, for example, that thederangements of the islands of our city, Venice. We will show you how to solve this kind of problems. Actually, they are all related to combinatorics. That is, counting the number of elements of a set. It sounds easy. But very often, mistakes occur in this type of computations. True Alberto. But after years of teaching this topic, we developed a full proof method. Yes. We translate the problem, say, in counting the number of elements of a precise mathematical structure.
Skip to 2 minutes and 6 seconds And then it’s enough to apply a specific principle and it’s done. Simple! Let us start, follow us and learn how to count.