So if I … How many different combinations can I make if I take out 2 marbles• The answer can be found in the 2nd place of row 5, which is 10. Practical Uses for Pascal's Triangle Date: 2/27/96 at 20:14:58 From: Andrew Cotton Subject: Help with Pascal's Triangle Hi, I teach 7th grade math. there are alot of information available to this topic. Expand Using Pascal's Triangle (x+3)^4. https://medium.com/i-math/top-10-secrets-of-pascals-triangle-6012ba9c5e23 All I have been able to find has been related to probability. Pascal's Triangle, named after French mathematician Blaise Pascal, is used in various algebraic processes, such as finding tetrahedral and triangular numbers, powers of two, exponents of 11, squares, Fibonacci sequences, combinations and polynomials. So Pascal's triangle-- so we'll start with a one at the top. Application - Combination• Pascal’s triangle can also be used to find combinations:• If there are 5 marbles in a bag, 1 red, 1blue, 1 green, 1 yellow and 1 black. And one way to think about it is, it's a triangle where if you start it up here, at each level you're really counting the different ways that you can get to the different nodes. Suppose that we want to find the expansion of (a + b) 11. Binomial Expansion Using Factorial Notation. some secrets are yet unknown and are about to find. Pascal’s Triangle is a triangular array of numbers where each number on the “interior” of the triangle is the sum of the two numbers directly above it. We have situations like this all of the time. Pascal's triangle. Pascal's Triangle can be displayed as such: The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding . So one-- and so I'm going to set up a triangle. Some of my students are trying to find "practical uses" for Pascal's triangle. We use the 5th row of Pascal’s triangle: 1 4 6 4 1 Then we have. Pascal's Triangle or Khayyam Triangle or Yang Hui's Triangle or Tartaglia's Triangle and its hidden number sequence and secrets. The disadvantage in using Pascal’s triangle is that we must compute all the preceding rows of the triangle … It was named after French mathematician Blaise Pascal. Pascal's triangle is an array of numbers that represents a number pattern. The coefficients will correspond with line of the triangle. For example, say you are at an ice cream shop and they have 5 different ice creams. REAL LIFE with Pascal’s Triangle One real life situation that Pascal’s Triangle is used for is Probability, and combinations. There are many interesting things about the Pascal’s triangle. One use of Pascal's Triangle is in its use with combinatoric questions, and in particular combinations. It has a number of different uses throughout mathematics and statistics, but in the context of polynomials, specifically binomials, it is used for expanding binomials.. 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