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Unformatted text preview: 16 Counting (cont.) 16.1 Solving problems by applying basic principles • often there are restrictions e.g. third letter must be A or E first digit must not be zero usually best to deal with restrictions first often helpful to use boxes • e.g. arrangements of all letters of BLISTER no restriction start with B end with a vowel • e.g. 3-digit numbers from digits 02468 implied restriction: first cannot be zero • another common restriction values must be adjacent e.g. arrangements of 12345 in which 1 and 2 are adjacent • another common variation elements in a circle illustrate with ABC in a circle only 2 arrangements generally use one value as a marker arrange others relative to the marker 16.2 The addition or sum rule • If one operation can be performed in m ways or a second operation can be performed in n ways, and only one of the operations can be performed , then the number of possible operations is m + n • in set terms given sets A and B with A ∩ B = ∅ , | A ∪ B | = | A | + | B | • this rule is often useful with a complement of a restriction...
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This note was uploaded on 04/19/2008 for the course ECE 190 taught by Professor Carter during the Fall '06 term at University of Toronto.
- Fall '06