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.
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