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Counting Principle

If one event can occur in m ways and a second can occur in n ways, the pair of events can occur in mn ways.

Example 1:

There are 4 roads from Carleton to Washington and 6 roads from Washington to Hareton. How many Carleton-Washington-Hareton routes are possible?

Answer: Each of the 4 roads from Carleton to Washington has 6 different choices. So, the total number of routes is 4 x 6 = 24

Example 2:
A baseball team has 6 pitchers and 3 catchers. How many different pitcher-catcher combination are there?

Answer: For each of the 6 pitchers there are 3 catchers; so there are 18 combinations.

Example 3:
In how many ways can 10 multiple-choice questions be answered if each question has 4 choices and each question is answered? if 2 questions are left unanswered?

Answer: If all questions were answered then there are 10 x 4 = 40 ways; if 2 questions were unanswered then there are 8 x 4 = 32 ways.

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