lesson 57 - The fundamental counting principles

Fundamental Counting Principle:
If one item can be selected in m ways, and for each way a second item can be selected in n ways then the two ways can be selected in mn ways.

Example 1: 
How many different two digit numbers are there?

  9       x   10      = 90
^                ^  0,1,2,3,4,5,6,7,8,9     <  these are your choices
1,2,3,4,5,6,7,8,9

Example 2: 
A multiple-choice test has 7 questions, with 4 possible answers for each question. Suppose students answer each question by guessing randomly.

a) How many possible answers are there for each question?
        4    
b) How many different patterns are possible for the answers to the 7 questions on the test?
    4 x 4 x 4 x 4 x 4 x 4 x 4 = 16384 
c) What is the probability that all 7 questions will be answered correctly?
    1/ 16384