give to their friends for his birthday party. There are 3 types of cards in the store, and he likes them all. In how many ways can he buy the 20 cards? It is required to choose a sample of 20 invitation cards out of the set of 3 types of cards, so and . The order in which you choose the different types of invitations does not matter. As a type of card must be selected more than once, there will be repetitions in our invitation cards. So, we want to select a non ordered sample of 20 elements () out of a set of 3 elements (), in which repetition is allowed. That is all we need to know to choose the right operation, and the result is: Distribution In a distribution problem it is required to place k objects into n boxes or recipients. In order to choose the right operation out of the ones that the model provides, it is necessary to know: Whether the objects are distinguishable or not. Whether the boxes are distinguishable or not. If the order in which the objects are placed in a box matters. The conditions that the distribution must meet. Depending on this, the distribution can be: Injective distribution: every box must have at most 1 object () Surjective distribution: every box must have at least 1 object () Bijective distribution: every box must exactly 1 object () Distribution with no restrictions The following table shows the operations that the model provides to get the number of different ways of distributing the objects for each of the distributions: Stirling numbers of the second kind Number of partitions of the integer k into n parts Lah numbers (Stirling numbers of the third kind) Examples 1.- A maths teacher has to give 3 studentships among his students. 7 of them got an 'outstanding' grade, so they are the candidates to get them. In how many ways can he distribute the grants? Let's consider the 3 studentships are objects that have to be distributed into 7 boxes, which are the students. As the objects are identical studentships, they are indistinguishable. The boxes are distinguishable, as they are different students. Every studentship must be given to a different student, so every box must have at most 1 object. Furthermore, the order in which the objects are placed in a boxes does not matter,