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f2006lecNotesWeek07 - 16 16.1 Counting(cont Solving...

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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 e.g.
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