Lesson Worksheet: Pascal’s Triangle Mathematics

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


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


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

  • A21
  • B2
  • C2
  • D21
  • E2


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


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


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

Given that 5,985 is the 18th element on the 22nd row, find 𝑎, 𝑏, 𝑐, 𝑑, 𝑒, and 𝑓.

  • A𝑎=20,349, 𝑏=4,845, 𝑐=1,140, 𝑑=1,330, 𝑒=7,315, 𝑓=26,334
  • B𝑎=21,546, 𝑏=4,845, 𝑐=1,140, 𝑑=1,260, 𝑒=7,245, 𝑓=27,531
  • C𝑎=20,349, 𝑏=4,560, 𝑐=1,425, 𝑑=1,330, 𝑒=7,315, 𝑓=26,334
  • D𝑎=20,349, 𝑏=5,130, 𝑐=855, 𝑑=1,330, 𝑒=7,315, 𝑓=26,334
  • E𝑎=21,546, 𝑏=5,130, 𝑐=855, 𝑑=1,260, 𝑒=7,245, 𝑓=27,531


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

  • A2
  • B2
  • C21
  • D2
  • E2


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.

  • A764
  • B732
  • C716
  • D7128
  • E7256


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.


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 345?


Use Pascal’s triangle to find the binomial expansion of (𝑥+𝑦).

  • A𝑥+4𝑥𝑦+6𝑥𝑦+4𝑥𝑦+𝑦
  • B2𝑥+4𝑥𝑦+6𝑥𝑦+4𝑥𝑦+2𝑦
  • C𝑥+4𝑥𝑦6𝑥𝑦+4𝑥𝑦
  • D𝑥4𝑥𝑦6𝑥𝑦4𝑥𝑦
  • E𝑥4𝑥𝑦6𝑥𝑦4𝑥𝑦+𝑦

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