Chapter 4: Combinatorics Notes

Sections

1. 4A Factorial notation Mastered

   The definition of n!, why 0! = 1, unrolling factorials, and simplifying and cancelling expressions with factorials.

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2. 4B Ordered selections Mastered

   The multiplication principle with boxes, ordered selections with repetition (n to the power r) and without repetition (nPr), permutations of a whole set, and dealing with restrictions first.

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3. 4C Grouping, complementary and cases Mastered

   Three more counting principles for ordered selections: treat objects that must be together as a block, count the complement, and split a problem into cases.

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4. 4D Arrangements with identical elements Mastered

   Count arrangements of objects where some are identical by dividing by the arrangements of each identical group, including words with repeated letters and patterns of two kinds of object.

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5. 4E Combinations Mastered

   Counting unordered selections with nCr, its formula and symmetry, and using it for committees, teams chosen from groups, and at least or at most questions.

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6. 4F Using counting in probability Mastered

   Find probabilities by counting the sample space and the event space with permutations and combinations, using the complement and a mix of methods.

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7. 4G Arrangements in a circle Mastered

   Count arrangements around a circle by fixing one person, arrange groups around a circle, and find probabilities for circular arrangements.

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