Enter the row number and column number into the calculator to determine the value of the number at that position in Pascal's Triangle.

Pascal's Triangle Formula

The following formula is used to calculate the value of a specific number in Pascal's Triangle:

C(n, k) = n! / (k! * (n-k)!)

Variables:

  • C(n, k) is the value of the number at row n and column k in Pascal's Triangle
  • n is the row number in Pascal's Triangle
  • k is the column number in Pascal's Triangle

To calculate the value of a specific number in Pascal's Triangle, divide the factorial of the row number (n!) by the product of the factorials of the column number (k!) and the difference between the row number and the column number (n-k)!.

What is a Pascal's Triangle?

Pascal's Triangle is a mathematical concept that presents a triangular array of binomial coefficients. It is named after the French mathematician Blaise Pascal, although other mathematicians had studied it centuries before him in India, Persia, China, and Italy. The triangle is constructed by starting with an apex of 1. Each subsequent row is created by adding the number above and to the left with the number above and to the right, treating blank entries as 0. The rows of Pascal's Triangle are conventionally enumerated, starting with row n = 0 at the top. The entries in each row are numbered from the left, beginning with k = 0, and are usually staggered relative to the numbers in the adjacent rows. The triangle may be used in various areas of mathematics, including algebra, probability theory, and combinatorics.

How to Calculate Pascal's Triangle?

The following steps outline how to generate Pascal's Triangle:

  1. Start with the first row, which contains only the number 1.
  2. For each subsequent row, add a 1 at the beginning and end.
  3. For each number in between, add the two numbers directly above it in the previous row.
  4. Repeat steps 2 and 3 until the desired number of rows is reached.

Example Problem:

Let's generate Pascal's Triangle with 5 rows.

Row 1: 1

Row 2: 1 1

Row 3: 1 2 1

Row 4: 1 3 3 1

Row 5: 1 4 6 4 1