Order Matters? Comb + Permu

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emitpeels

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Hey guys. I'm having some trouble with telling when to use the formula for a combination or a permutation. Whenever I read a question of how many different ways someone can eat an ice cream cone or something of that sort, I struggle with trying to figure out if order matters or not. Does anyone have any advice? I know its a simple problem, but I'm on the struggle bus with it for some reason.
 
The way they phrase the question is the key. So combination is where you don't count the order. Questions like how many possibilities that the boys and girls sit together, or that the committee has 3 boys and 2 girls; these are the combination questions. You can think of it as "as long as he's a boy he'll do". To be more specific, if you are to choose 3 girls from 5 girls named A B C D E, you would go with ABC BCD CDE ACD ACE etc, but not ABC BAC CAB (these three are the same) BCD CBD DBC. So the order should not count.

But for the questions like selecting a head for a school play or assign seats to the students, keep in mind that if Tom is assigned to be the head, then it's Tom's team; likewise if Sue is assigned, then it's Sue's team. They are different. So permutation is the case where if a different person is assigned/counted, the situation is different and can be counted as a possibility. Whereas in combination, if one element of the group is to be selected, it doesn't matter which one you select, as long as it satisfies the criteria, it won't change the count.

I hope this helps 🙂
 
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