Pascal's Triangle Exploration

Pascal's Triangle Exploration

Read each question carefully and answer to the best of your ability. Show all your work where applicable.

Pascal's Triangle is a triangular array of binomial coefficients. It starts with a single '1' at the top, and each number below is the sum of the two numbers directly above it. If there is only one number above, it's considered to be added to 0.

Here are the first few rows:

1 1 1 1 2 1 1 3 3 1 1 4 6 4 1

1. Complete the next two rows of Pascal's Triangle based on the pattern: 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1         1 1           1

2. What is the sum of the numbers in the 5th row of Pascal's Triangle (starting with row 0 as '1')?

3. Look at the second diagonal from either side of Pascal's Triangle (1, 2, 3, 4...). What type of numbers do you see?

4. All the numbers in Pascal's Triangle are odd.

5. Explain how Pascal's Triangle is related to combinations (e.g., choosing items from a set).