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    <title>counting on Ciência Programada</title>
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      <title>Sum Rule and Product Rule: The Foundation of Counting</title>
      <link>https://cienciaprogramada.com/2026/06/sum-and-product-rules/</link>
      <pubDate>Tue, 30 Jun 2026 00:00:00 +0000</pubDate>
      <author>contato[@]cienciaprogramada.com.br (Francisco Bustamante)</author>
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      <description>With 4 math books and 3 Portuguese books, there are 7 ways to pick one book and 12 ways to pick one of each. The first count is a sum and the second is a product: these are the sum rule and the product rule, applied here to passwords, flags, answer keys, and counting divisors.</description>
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      <title>The Art of Counting: A Journey Through Combinatorics</title>
      <link>https://cienciaprogramada.com/2026/06/the-art-of-counting/</link>
      <pubDate>Mon, 29 Jun 2026 00:00:00 +0000</pubDate>
      <author>contato[@]cienciaprogramada.com.br (Francisco Bustamante)</author>
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      <description>How many 8-character passwords are there? In how many ways can 10 people sit around a table? Combinatorics answers without listing every case. This is the roadmap of the series: from the counting rules to permutations, arrangements, combinations and the binomial theorem.</description>
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