Education Technology

### Mathematics lessons for IB® Diploma Programme

Applications and Interpretation | Statistics and Probability

# Too Many Choices

Students investigate the fundamental counting principle, permutations, and combinations.

## Step 1

Students will explore the fundamental counting principle and discover its formula. They will use diagrams to help them determine the number of different combinations of cake and frosting. After a discussion of the formula, students will use it to solve several problems.

## Step 2

Then, students will use the fundamental counting principle to discover the general formula for permutations. In this investigation students will determine the number of arrows that connect 2 points for a given number of possible points. After a discussion of the formula, students will use it to solve several problems.

## Step 3

Students will use the general formula for permutations to discover the formula for combinations. They will determine the possible combinations for a committee of 3 people selecting from 6 people. Then students will continue their investigation of the arrows by determining the number of edges, where the order of the arrows does not matter. After a discussion of the formula, students will use it to solve several problems.