![]() ![]() Either way, they’re equally disappointed. If I give a can to Alice, Bob and then Charlie, it’s the same as giving to Charlie, Alice and then Bob. Well, in this case, the order we pick people doesn’t matter. How many ways can I give 3 tin cans to 8 people? In fact, I can only afford empty tin cans. Let’s say I’m a cheapskate and can’t afford separate Gold, Silver and Bronze medals. If we have n items total and want to pick k in a certain order, we get:Īnd this is the fancy permutation formula: You have n items and want to find the number of ways k items can be ordered:Ĭombinations are easy going. Where 8!/(8-3)! is just a fancy way of saying “Use the first 3 numbers of 8!”. What’s another name for this? 5 factorial!Īnd why did we use the number 5? Because it was left over after we picked 3 medals from 8. This is where permutations get cool: notice how we want to get rid of $5 * 4 * 3 * 2 * 1$. Unfortunately, that does too much! We only want $8 * 7 * 6$. To do this, we started with all options (8) then took them away one at a time (7, then 6) until we ran out of medals. The total number of options was $8 * 7 * 6 = 336$. We picked certain people to win, but the details don’t matter: we had 8 choices at first, then 7, then 6. Silver medal: 7 choices: B C D E F G H.Gold medal: 8 choices: A B C D E F G H (Clever how I made the names match up with letters, eh?). ![]() We’re going to use permutations since the order we hand out these medals matters. How many ways can we award a 1st, 2nd and 3rd place prize among eight contestants? (Gold / Silver / Bronze) We’re using the fancy-pants term “permutation”, so we’re going to care about every last detail, including the order of each item. P(25,4) = 303,600 (Repeating numbers within a code would give 390,625 different codes.Let’s start with permutations, or all possible ways of doing something. How many different codes can we have if there are 25 different numbers and numbers cannot repeat in any given code? How possible orders can be made by choosing only 3 of the 18? At Waffle House hash browns can be ordered 18 different ways.How many different ways can this selection be done? A GM from a restaurant chain must select 8 restaurants from 14 for a promotional program.How many ways can a jury of 12 people be selected from a group of 40 people?.In how many ways can a chief executive officer, a director, and a treasurer be selected? A board of directors consists of 13 people.You Try!īased on what you just learned, can you spot the difference between a combination and permutation? Bonus points if you can calculate the result. But if numbers could repeat, there are 39*39*39 = 59,319 possible codes – to include repeatable values, apply the PERMUTATIONA function in Excel. If numbers couldn’t repeat, we’d have P(39,3) = 54,834 different codes (or what we call “combinations”). So how many possible codes does this locker have? Does order matter? Absolutely! If you try to open the lock using your 3 number code but in a different order, the locker will not open. Let’s assume a typical dial lock (Right, left, right) in which there are 39 numbers on the dial and your code has 3 numbers. How many possible verification codes can be produced? Let’s say your company requires a 5-value verification code consisting of 3 numerical values and 2 alphabetic values ( in that order and case sensitive). ![]() The fundamental counting principle says you now have: How many possible outfits can you make? (Assume they all match, or you are 5 years old and don’t give a flip.) Say you pack 4 shirts, 3 pairs of pants, and 2 pairs of shoes. The Fundamental Counting PrincipleĪlso known as the multiplication counting rule, this principle says to multiply all possible events together to find the total number of outcomes.Ī simple example starts with packing for a vacation. But first, I’ll discuss the Fundamental Counting Principle and factorials. In this post I’ll give you definitions, formulas, and examples of both permutations and combinations. The difference between a permutation and a combination is simple to understand – if you pay close attention to how the items/objects/people are chosen (and ignore semantics). This is especially helpful in probability when calculating a denominator and/or numerator. Permutations and combinations are useful to someone interested in determining the total number of items from a set or group. Welcome to the third installment of my Cheat Sheet for Stats. ![]() (and why your locker combination is actually a permutation) ![]()
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