This instructional aid was prepared by the Tallahassee Community College Learning Commons.
The Fundamental Counting Principle
Problems involving counting usually deal with ways of selecting objects, numbers, or people.
Sometimes these selections involve a need to order and/or a need to repeat. Order in an
experiment is essential when things, numbers, or persons must occupy a first position, a
second position, etc. License plate characters and “combination” lock numbers imply a need
for order or arrangement:
ABC 123 is a different license number from ABC 321.
Left 25-Right 13-Left 25 is a different lock “combination” from Left 25-Right
25-Left 13. (Note the repetition of 25)
Choosing 3 members for county commissioner from a field of 9 candidates involves no ordering
and no repetition.
The Fundamental Counting Principle is used when order is implied or stated, and repetition
may or may not be allowed.
The FCP uses the operation of multiplication. It involves drawing a "slot" for each possible
outcome, filling in the number of possibilities for each outcome, and then multiplying across.
Example 1
Two fair dice are rolled. How many different ways can they land? A fair die can have 6 possible
number outcomes: 1, 2, 3, 4, 5 or 6
Order underlies the experiment since a "2" on the 1st die and a "4" on the 2nd die is a different
outcome from a "4" on the 1st and "2" on the 2nd. Repetition is implied in this experiment
since the outcomes of the 2 dice are independent of each other.
The table shows the 36 possible outcomes.
