Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License. Use the information below to generate a citation. Then you must include on every digital page view the following attribution: Spectrophotometry is a technique that uses light absorption to measure the concentration of an analyte in solution. If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses the Consider this set of objects ( Figure 7.3): If we have a set of objects to be counted that can be physically arranged into a rectangular shape, then we can use multiplication to do the counting for us. One of the first combinatorial short cuts to counting students learn in school has to do with areas of rectangles. For example, in the t-shirt problem above, the two sets are size and color, and since there are 4 possible sizes and 2 possible. Multiplication as a Combinatorial Short Cut Students also learn the Counting Principle, which states that when one item is selected from each of two or more sets, the total number of possible outcomes is equal to the product of the number of items in each set. These techniques fall under the mathematical discipline of combinatorics, which is devoted to counting. So, mathematicians have developed short cuts to counting big numbers. One of the first bits of mathematical knowledge children learn is how to count objects by pointing to them in turn and saying: “one, two, three, …” That’s a useful skill, but when the number of things that we need to count grows large, that method becomes onerous (or, for very large numbers, impossible for humans to accomplish in a typical human lifespan).
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