# Permutations and Combinations

Learn about permutations and combinations.

StartPermutations and Combinations: Lesson

Lesson 1 of 1

- 1An
*enumeration*is defined as the number of ways to select from, or arrange, a set of*n*objects. Before we can begin studying this process, we have to explore some fundamental concepts. Let’s … - 2An ice cream parlor offers 27 different flavors of ice cream! Customers are allowed to fill their ice cream cone with three flavors of their choosing. How many different ice cream treats can be con…
- 3In this lesson, we will explore the concept of a permutation. A
*permutation*is an arrangement or selection in which the order matters. Consider this scenario: a college student has just purchase… - 4In the previous exercise, you learned how to compute the number of permutations of
*n*items. What if you were only interested in the permutation of*r*out of those*n*items (permutation of four … - 5Until now, we have considered enumerations where the order of arrangement or selection matters. In the last exercise, one flight itinerary chosen could be New York, Virginia, Florida, Louisiana, Te…
- 6In this exercise, we will explore how to enumerate elements of a
*multiset*(a set that contains elements that are not necessarily distinct). Consider the problem of having to determine the number … - 7In this exercise, we will explore problems in which we have to choose
*r*items from*n*different varieties. Consider this example: a taco restaurant offers three options of taco to choose from. Y… - 8When enumerating a multiset, we are sometimes interested in the relative order of some members of the set. Take for example the problem of figuring out how many ways we can order the letters in the…
- 9So far, you have learned many techniques to enumerate members of a set. Well done! In a real-world problem, however, arranging or selecting from a set of items may not be so straightforward. A sing…
- 10If we want to find out the number of ways NOT to do something, we could break it down into the subcases that are allowed and then combine those. Sometimes this may be inefficient as there might be …

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