Isye 2027

# So the number of possibilities is 4 3 2 1 4 read four

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Unformatted text preview: sible bytes is 28 . (Each byte represents a number in the range 0 to 255 in base two representation.) The idea behind the principle of counting is more general than the principle of counting itself. Counting the number of ways to assign values to variables can often be done by the same approach, even if the choices are not independent, as long as the choice of one variable does not aﬀect the number of choices possible for the second variable. This is illustrated in the following example. Example 1.3.2 Find the number of four letter sequences that can be obtained by ordering the letters A, B, C, D, without repetition. For example, ADCB is one possibility. Solution: There are four ways to select the ﬁrst letter of the sequence, and for each of those, there are three ways to select the second letter, and for each of those, two ways to select the third letter, and for each of those, one way to select the ﬁnal letter. So the number of possibilities is 4 · 3 · 2 · 1 = 4! (read “four factorial...
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