5: Counting with Repetitions
- Page ID
- 60209
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In counting combinations and permutations, we assumed that we were drawing from a set in which all of the elements are distinct. Of course, it is easy to come up with a scenario in which some of the elements are indistinguishable. We need to know how to count the solutions to problems like this, also.
- 5.1: Unlimited Repetition
- For many practical purposes, even if the number of indistinguishable elements in each class is not actually infinite, we will be drawing a small enough number that we will not run out. We’ll consider two scenarios: the order in which we make the choice matters, or the order in which we make the choice doesn’t matter.
- 5.2: Sorting a Set that Contains Repetition
- In the previous section, the new work came from looking at combinations where repetition or replacement is allowed. In this section, we’re going to consider the situation where there are a fixed number of objects in total; some of them are “repeated” (that is, indistinguishable from one another), and we want to determine how many ways they can be arranged (permuted). This can arise in a variety of situations.
- 5.3: Summary
- This page contains the summary of the topics covered in Chapter 5.