because there cannot be more than one on each box. So, it is a non ordered injective distribution of 3 indistinguishable objects () into 7 distinguishable boxes (). That is all we need to know to choose the right operation, and the result is: 2.- A group of 8 friends rent a 5-room cottage to spend their holidays. If the rooms are identical and no one can be empty, in how many ways can they be distributed in the cottage? Let's consider the friends are objects that have to be distributed into 5 boxes, which are the rooms. As the objects are different people, they are distinguishable. The boxes are indistinguishable, as they are identical rooms. We can consider it as a non ordered distribution, because the ordered in which everyone is placed in the rooms does not matter. No room can be empty, so every box must have at least 1 object. So, it is a non ordered surjective distribution of 8 distinguishable objects () into 5 indistinguishable boxes (). That is all we need to know to choose the right operation, and the result is: 3.- 12 people are done shopping in a supermarket where 4 cashiers are working at the moment. In how many different ways can they be distributed into the checkouts? Let's consider the people are objects that have to be distributed into boxes, which are the check-outs. As the people and the checkouts are different, the objects and the boxes are distinguishable. The order in which the objects are placed in the boxes matter, because they are people getting into queues. The statement does not mention any restriction. So, it is an ordered distribution with no restrictions of 12 distinguishable objects () into 4 distinguishable boxes (). That is all we need to know to choose the right operation, and the result is: Partition A partition problem requires to divide a set of k elements into n subsets. This model is related to the distribution one, as we can consider the objects inside every box as subsets of the set of objects to distribute. So, each of the 24 distributions described previously has a matching kind of partition into subsets. So, a partition problem can be solved by transforming it into a distribution one and applying the correspondent operation provided by the distribution model (previous table). Following this method, we will get the number