Counting And Probability
Rules for Counting
There are two basic rules for counting which can deal with most problems. We phrase the rules in terms of ``jobs" which are to be done.
The Addition Rule:
Suppose we can do job 1 in P ways and job 2 in Q ways. Then we can do either job 1 or job 2, but not both, in P+Q ways.
1. For example, suppose a class has 30 men and 25 women. There are 30+25=55 ways the professor can pick one student to answer a question.
The Multiplication Rule:
Suppose we can do job 1 in P ways and an unrelated job 2 in Q ways. Then we can do both job 1 and job 2 in PxQ ways.
2. For example, to ride a bike, you must have the chain on both a front sprocket and a rear sprocket. For a 21 speed bike there are 3 ways to select the front sprocket and 7 ways to select the rear sprocket.
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