Pascal's Triangle is more than just a big triangle of numbers with patterns and stuff. There are two major areas where Pascal's Triangle is used, in Algebra and in Probability / Combinatorics. Below is a detailed explanation of Probability/Combinations. Understand the following and you'll never know when this handy triangle will come in useful for your schoolwork or officework!
The other main area where Pascal's Triangle shows up is in Probability, where it can be used to find Combinations. Let's say you have five coats in your closet, and you want to know how many different ways you can pick two of them and wear them. It doesn't matter to you which coat is in front, it just matters which two hats you pick. So this problem amounts to the question "how many different ways can you pick two objects from a set of five objects?"
The convenctional method is to take 4+3+2+1, which is equal to 10. However you can do the same with Pascal's Triangle. The Pascal's Triangle method not only requires less thinking but doesn't waste time either. Well, here's how you do it.
The Answer: It's the number in the third place in the Row 5, i.e. 10. (Remember that the Row 5 is the sixth line of numbers. Consists of numbers 1, 5, 10, 10, 5, 1)