Pascal's Triangle Exploration

Pascal's Triangle Exploration

Follow the instructions for each section. Show all your work where applicable.

Pascal's Triangle is a triangular array of the binomial coefficients. It is named after the French mathematician Blaise Pascal. Each number is the sum of the two numbers directly above it.

The first few rows of Pascal's Triangle are shown above. Notice the '1's along the edges and how each inner number is the sum of the two numbers directly above it.

1. Complete the next two rows of Pascal's Triangle below:

Row 0: 1

Row 1: 1 1

Row 2: 1 2 1

Row 3: 1 3 3 1

Row 4: 1 4 6 4 1

Row 5: 1         1

Row 6: 1           1

2. What is the sum of the numbers in Row 4 of Pascal's Triangle?

3. Which of the following sequences can be found along the diagonals of Pascal's Triangle?

4. How can Pascal's Triangle be used to find the coefficients of the expansion of (a + b)³?

5. All numbers in Pascal's Triangle are odd.

6. The numbers in each row of Pascal's Triangle are symmetrical.

7. A coin is tossed 5 times. Use Pascal's Triangle to determine how many different ways you can get exactly 3 heads.