Counting Principles

The Fundamental Counting Principle states that
if event M can occur in m ways and event N can occur in n ways, then event M followed by event N can occur in m · n ways.

If event M can occur in 3 ways and event N can occur in 4 ways, then M followed by N can occur in 3 ·4 or 12 ways.

A nurse has three patients to visit. How many different ways can she make her rounds if she checks each patient once? Answer

High school faculty are to be issued special coded identification cards that consist of four letters of the alphabet. How many different ID cards can be issued if the letters can be used more than once? Answer

Suppose now that the letters in the high school identification codes cannot be repeated, how many different identification cards can be created? Answer

The digits 0, 1, 2, 3, and 4 are to be used in a 4-digit ID card. How many different cards are possible if repetitions are permitted? Answer

The digits 0, 1, 2, 3, and 4 are to be used in a 4-digit ID card. How many different cards are possible if repetitions are not permitted? Answer

Kayla is in charge of a talent show at BHS. There are eight contestants. She must choose in what order they will appear. How many different ways can she schedule the performers? Answer

Test your understanding of the Fundamental Counting Principle.
Practice Problems