Counting
One stage can be accomplished in A ways
Another can be accomplished in B ways
Another can be accomplished in C ways
…and so on, then the total number of ways to accomplish the task is
When tackling a counting problem:
Identify/list possible outcomes
Determine whether the task can be broken into stages
Determine the number of ways to accomplish each stage, beginning with the most restrictive stage(s)
Apply the Fundamental Counting Principle
Factorial notation:
n unique objects can be arranged in n! ways. Example: There are 9 unique letters in the word wonderful, so we can arrange its letters in 9*8*7*… = 362,880 ways.
Restrictions:
Arranging objects when some are alike
Given n objects where A are alike, another B are alike, another C are alike and so on.
Combinations:
When the order does not matter – for example, picking any 3 friends from a group of 5.
Permutations:
When the order does matter – for example, how many ways you could order 3 letters from the word PARTY?
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