# Lesson Worksheet: Pascal’s Triangle Mathematics

In this worksheet, we will learn how to solve problems on Pascal’s triangle.

**Q1: **

In the picture of Pascal’s triangle shown, what type of numbers appear in the diagonal indicated by the arrow?

- AThe Fibonacci numbers
- BThe cube numbers
- CThe square numbers
- DThe triangular numbers

**Q2: **

What is the sum of the terms in the 30th row of Pascal’s triangle?

- A
- B
- C
- D
- E

**Q3: **

The figure shows a section of Pascal’s triangle. Without using a calculator, find the sum of the highlighted elements.

**Q4: **

What is the second element in the 500th row of Pascal’s triangle?

**Q5: **

The figure shows 7 adjacent elements in Pascal’s triangle.

Given that 5,985 is the 18th element on the 22nd row, find , , , , , and .

- A, , , , ,
- B, , , , ,
- C, , , , ,
- D, , , , ,
- E, , , , ,

**Q6: **

What is sum of every other element in the 1,000th row of Pascal’s triangle?

- A
- B
- C
- D
- E

**Q7: **

James is playing a game where a ball is dropped onto an array of pegs, from vertically above the top peg, and it bounces down to numbered buckets at the bottom.

He only gets a prize if it falls into buckets 3 or 7. Find the probability that he gets a prize given that there is an even probability it will fall to the left or the right of any given peg.

- A
- B
- C
- D
- E

**Q8: **

You have 7 pool balls. Find, using Pascal’s triangle, how many different ways you could choose just 3 of them, ignoring the order that you select them in.

**Q9: **

In Pascal’s triangle, each entry is the sum of the two entries above it. In which row of Pascal’s triangle do three consecutive entries occur that are in the ratio ?

**Q10: **

Use Pascal’s triangle to find the binomial expansion of .

- A
- B
- C
- D
- E