You may be wondering then, how is this different from the method to compute all the possible arrangements of a list of items side by side that we have seen before? Well, in simple words, when all of the objects from the set will be arranged side by side, permutations produce the total quantity exactly in the same way as we have calculated it before, the difference comes when you have a list of items and you will not be arranging them all. A permutation refers to this order and all of the possible arrangements of the items according to specific conditions, which limit the amount of items from the set that will be used in the arrangements. Let us explain, we have seen example problems where we had to find out all of the different possible arrangements of items from a set that are ordered side by side. If you think about it, it sounds exactly the same as what we have seen before in our lesson about factorials, because it actually is in specific cases! The idea of permutation is rooted in the process of arranging and finding how many total possible arrangements exist for a group of items in a set. Without further ado, let us start by introducing permutations and combinations separately. Therefore, we have decided to dedicate this lesson to introduce both concepts together, the permutation and the combination, and later, we will have a lesson dedicated to each one and a variety of example problems to practice them further. After our lesson on factorials we are ready to learn about the most important part of combinatorics: permutations and combinations in reality, what we learned about the factorial notation in our past lesson (please make sure you read that lesson first!) provides the basis for these two new concepts, which are deeply intertwined with each other.
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