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Imagine a group of 12 sprinters is competing for the gold medal.
What is the probability of winning the National Lottery?
Do you know the difference between permutation and combination? Yet, what I’ve noticed over the years is it’s not so much both of them that are the issue as it is which one to use for a particular problem: the combination vs permutation question.
Finally, that leaves us with 10 athletes for the bronze medal podium.
The math looks like this:12 x 11 x 10 = 1320You might notice that this is the fundamental counting principle.
Your job is not to solve the question but to determine whether you use the combinations or the permutations formula to solve them.1. Had she been choosing five panels from a total of 8, let’s say, then we would need to use combinations.2.
Joan has five panels at home that she wants to paint. Permutations Okay, this was a little bit of a trick, since I used the word “combinations”. Combinations We are choosing a group from a larger group.How many different ways can the letters P, Q, R, S be arranged? The second space can be filled by any of the remaining 3 letters. This is because there are four spaces to be filled: _, _, _, _ The first space can be filled by any one of the four letters.How many different ways can these three medals be handed out? Even though the top three spots for the sprinters forms a subgroup, it is the ordering within that subgroup that matters greatly, and is the difference between a gold, silver, and a bronze medal. Now, we have one athlete fewer—since one is already on the gold medal podium.An easy way to solve this question mathematically is to imagine that the dashes below are the podium upon which each sprinter will stand (albeit the dashes are at the same level):____ ____ ____ gold silver bronze To find out the number of different arrangement, ask yourself how many athletes can stand on the gold medal podium? So that gives us a total of 11 for the silver medal spot.She has five different colored paints and intends to paint each panel a different color. But that word I used colloquially, not mathematically. One way to think of it is that when you use the word choose in the context of selecting from a group, you are dealing with combinations.How many different ways can she paint the five panels? How many unique combinations of the word MAGOOSH can I form by scrambling the letters? There are seven astronauts who are trying out to be part of three-person in-space flight team. And “choose” and “combinations” both begin with the letter ‘C’.For instance, if I’m a basketball coach and I want to find out how many distinct teams I can form based on a group of people, I want to use combinations.To make sure you understand this important distinction, here are three different scenarios.It’s a good question, so what I want you to do is imagine that you have 3 shirts and 3 pants. My advice is to try about 5 or 6 more combinations/permutations problems so that you can get the hang of it.How many different shirt-pants getups can you wear? With a little practice, you’ll able to deal with most of the problems the GRE hands you.