Combinatorial modelling is the process which lets us identify a suitable mathematical model to reformulate a problem. These combinatorial models will provide, through the combinatorics theory, the operations needed to solve the problem. Implicit combinatorial models Simple combinatorial problems are the ones that can be solved by applying just one combinatorial operation (variations, permutations, combinations, …). These problems can be classified into three different models, called implicit combinatorial models. Selection A selection problem requires to choose a sample of k elements out of a set of n elements. It is needed to know if the order in which the objects are selected matters and whether an object can be selected more than once or not. This table shows the operations that the model provides to get the number of different samples for each of the selections: Examples 1.- At a party there are 50 people. Everybody shakes everybody’s hand once. How often are hands shaken in total? What we need to do is calculate the number of all possible pairs of party guests, which means, a sample of 2 people out of the 50 guests, so and . A pair will be the same no matter the order of the two people. A handshake must be carried out by two different people (no repetition). So, it is required to select an ordered sample of 2 elements out of a set of 50 elements, in which repetition is not allowed. That is all we need to know to choose the right operation, and the result is: 2.- Unfortunately, you can’t remember the code for your four-digit lock. You only know that you didn’t use any digit more than once. How many different ways do you have to try? We need to choose a sample of 4 digits out of the set of 10 digits (base 10), so and . The digits must be ordered in a certain way to get the correct number, so we want to select an ordered sample. As the statement says, no digit was chosen more than once, so our sample will not have repeated digits. So, it is required to select an ordered sample of 4 elements out of a set of 10 elements, in which repetition is not allowed. That is all we need to know to choose the right operation, and the result is: 3.- A boy wants to buy 20 invitation cards to