When a problem is too complicated to be represented by a probability tree diagram or Venn diagram, counting techniques such as those introduced in Unit 2 are used.

 Math 30-2 Diploma Exam has 28 multiple-choice items. Each contains 4 choices. Many students do not complete exam items in order. They prefer to find simpler questions to complete first. How many different combinations are there to complete the test, assuming all questions are answered? If a student was to guess on every question, what is the probability that a student would select all the answers correctly?  

 

Each item has 4 responses the student could choose; thus, 4 ways are available to choose a response for each item. Use the Fundamental Counting Principle to determine the total number of ways to respond to the items on the test. There are 28 tasks, each having 4 choices.

4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x4x=4 28

The total number of ways to answer the twenty-eight items is .

The probability of guessing all the correct responses is 1.4 × 10 -17 .

This means the student has a better chance to win the lottery than to guess all the answers correctly!