Section 5.4 Summary

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  1. The Multiplication Rule for Counting provides the total number of different possible outcomes for a series of events.
  2. A permutation is an arrangement in which
    • items are chosen from distinct items.
    • repetition of items is not allowed.
    • the order of the items is important.

    In a permutation, order is important. In a combination, order does not matter. A combination is an arrangement in which

    • items are chosen from distinct items.
    • repetition of items is not allowed.
    • the order of the items is not important.
  3. Combinations may be used to calculate certain probabilities. For such problems, use the following steps:
    • Step 1 Confirm that the desired probability involves a combination.
    • Step 2 Find , the number of outcomes in event E.
    • Step 3 Find , the number of outcomes in the sample space.
    • Step 4 Assuming that each possible combination is equally likely, find the probability of event as follows: