# Essay On Pascal Triangle

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Real World Applications There are many real-world applications using the Pascal Triangle. The most popular is in algebra for expanding the binomial (x+y)ⁿ, where “n” is a specific exponent. Another way the triangle can be used is to calculate probability or determine the odds. The triangle is also full of interesting and functional mathematical patterns that can be used in solving a variety of other equations and figuring out numerical problems. “A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial” (Russell, n.d.). Binomials are used in algebra and are most commonly represented by the letters (a, b) or (x, y). As you continue to multiply (a+b) by itself to solve the equation, mathematical calculations become longer and longer. For example, an equation with a larger exponent “n” would take a long time to multiply out by hand. A quicker way to solve or expand the binomial is to use the Binomial Theorem. As it turns out, the numbers of the coefficients are the same as the numbers in Pascal’s Triangle. The numbers in the triangle can actually be used to expand binomial coefficients…show more content…
There are only two possible outcomes from a coin toss: heads or tails and the number of times you toss the coin will determine how many different combinations are possible. So, the question is “What is the probability of getting exactly two heads with only 4 coin tosses?” By looking at the 4th row of Pascal’s Triangle, the numbers are 1,4,6,4,1 and added together equal 16. The middle number is 6 so the probability is 6/16 or 37.5%. The long way to prove the answer is to write out all the possible outcomes and you can see from the chart below there are 16 possible outcomes for the 4 coin tosses and only 6 of them have exactly 2 heads which means the probability is 6/16 or 37.5% (Pascal’s Triangle,