Counting Theory: Lesson
Lesson 1 of 1
  1. 1
    Introduction
    There are three types of people, those who can count and those who can’t! Counting the number of ways to perform a task is simple — until the number of choices gets too large. One fundamental cou…
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  2. 2
    The Rules of Sum and Product
    It takes some mathematical insight to figure out how many elements satisfy a property without enumerating all of them. Here are some standard techniques. * The Sum Rule: If there are n(P) ways to …
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  3. 3
    Extending the Counting Rules
    What if there are many groups, and not just two? For example, a test consists of six multiple-choice questions. Each question has four possible answers. How many possible answer combinations are th…
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  4. 4
    Principle of Inclusion-Exclusion
    The choices we have seen till now are from disjoint groups. For example, the same food item is not both a crust and a topping. The two groups are independent of each other. Let us look at another…
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  5. 5
    Pascal's Triangle
    One very interesting number pattern is Pascal’s Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). To build the triangle, start with a ‘1’ at the top, then continu…
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  6. 6
    Applications of Counting Theory
    #### Bit strings A bit string is a sequence of bits (0 or 1). For example, 00001111 and 1011010 are bit strings of length 7. Bit strings can be used to represent sets or to manipulate binary data….
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  7. 7
    Review
    Here’s a summary of what we’ve learned: 1. If there are p ways to do one thing, and q ways to do another independent thing, then there are p * q ways to do both things. 2. If there are p…
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