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counting1

# counting1 - 1 Counting Basic principles for counting the...

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Unformatted text preview: 1 Counting Basic principles for counting the number of elements in a set. 1. Count each element once. 2. Don’t count an element more than once. 3. Determine how elements differ, and apply the appropriate rule. Notation: S , S 1 , S 2 , ... are sets | S | = the number of elements in S . The Sum Rule Conditions: • S = S 1 ∪ S 2 • S 1 ∩ S 2 = ∅ • | S 1 | = n 1 • | S 2 | = n 2 Conclusion: | S | = n 1 + n 2 . Example: S = set of alphanumeric characters S 1 = set of digits, and S 2 = set of letters S = S 1 ∪ S 2 , and S 1 ∩ S 2 = ∅ | S 1 | = 10, and | S 2 | = 26 (ignoring case) Therefore, | S | = 10 + 26 = 36 2 The Product Rule Conditions: • S = S 1 × S 2 • | S 1 | = n 1 • | S 2 | = n 2 Conclusion: | S | = n 1 * n 2 . Example: S = two digit numbers, no leading zeroes S 1 = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } S 2 = { , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 } | S 1 | = 9 and | S 2 | = 10 Therefore, | S | = 9 * 10 = 90 The Inclusion-Exclusion Principle Conditions: •...
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counting1 - 1 Counting Basic principles for counting the...

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