Counting theory

• partitions

• permutations

• combinations

Counting is used to determine the number of objects with certain properties. For examples: The number of SIM cards a company has to produce if they've been assigned 7 digit numbers. Number of possible match starters (football, basketball) given the number of team members and their positions.

Basic counting rules

• Counting problem may be complex, so simplify it using decomposition.

• Basic decomposition rules:

  • Product rule

    count decomposes into a sequence of dependent counts; each element in the first count is associated with all elements of the second count.

  • Sum rule

    count decomposes into a set of independent counts; elements of counts are alternatives.

Techniques for determining, without direct enumeration, the number of possible outcomes of particular event or the number of elements in a set. Such counting is sometimes called combinatorial analysis. It includes the study of permutations and combinations.