Option #1:Counting Principles #1. Mathematics & Economics Math Problem

Option #1: Counting Principles #1
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Introduction
The counting principles focus on diverse forms of groupings elements of a set, forming them and calculating. Marking these groupings depends on whether the elements are repeated, whether all the elements are used and whether there is ordering the elements or not. The available elements form a group where the permutations and combinations formulas are among the most common. The permutations can be with or without repetition, and the permutations consist of grouping elements when the order and elements are considered, and these elements may be repeated. The combination may also be with or without repetition, and in combinations, the order does not matter, unlike permutation where the order matters. This paper answers the three questions in Option #1 of Counting Principles #1, providing calculation, explanations, and summary of the three scenarios.
Counting Principles
When there are eight tomato varieties are listed in a seed catalog, and one can select five packages of tomato seeds the available choices are a form of permutation. This is a case of permutations without repetition, where the number of options in each step is reduced (Brase & Brase, 2018). One would first choose eight possibilities, then 7, 6, 5 and four possibilities. The factorial function (!) indicates that descending numbers are multiplied, and when there are repetitions in permutations the orders matter and the elements are repeated
The results are 8P5 (8! / 3/!), which is (40,320/ 6) or 8 x 7 x 6 x 5 x 4 =6720
To creat...