Section 5.4 Summary

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: