# Isye 2027

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Unformatted text preview: die is rolled, with X representing the side showing on the coin (H for heads or T for tails) and N being the number showing on the die. For example, {H, 3}, or H 3 for short, corresponds to the coin showing heads and the die showing three. The set of all possible 1.3. CALCULATING THE SIZE OF VARIOUS SETS 13 outcomes can be listed as: H1 H2 H3 H4 H5 H6 T 1 T 2 T 3 T 4 T 5 T 6. Obviously there are twelve possible outcomes. There are two ways to choose X, and for every choice of X, there are six choices of N. So the number of possible outcomes is 2 × 6 = 12. This example is a special case of the principle of counting: If there are m ways to select one variable and n ways to select another variable, and if these two selections can be made independently, then there is a total of mn ways to make the pair of selections. The principle extends to more than one variable as illustrated by the next example. Example 1.3.1 Find the number of possible 8-bit bytes. An example of such a byte is 00010100. Solution: There are two ways to select the ﬁrst bit, and for each of those, there are two ways to select the second bit, and so on. So the number of pos...
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## This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.

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