you use the combinations formula if "order doesn't matter", and you use the permutations formula if "order matters".
you could figure this out for yourself - just throw some numbers into the 2 formulas and notice that the combinations formula gives a smaller result. since there are more possibilities if "order matters" (because simply rearranging objects gives "new possibilities" in that case), the larger number must correspond to the case where "order matters" and the smaller number to the case where "order doesn't matter".
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the reason i've been enclosing "order matters" in scare quotes is that the concept of "order" can get confusing at times. here's a less ambiguous way to think about it:
if rearranging the elements in a set produces a new outcome, then use permutations. if not, then use combinations.
here's what i mean:
let's say you're going to randomly read 5 pages of a ten-page bulletin. now, because the pages are numbered, your first instinct is probably to say that "order matters". however, that's not the case: for instance, if i pick pages 1, 4, 5, 6, and 8, then that's the SAME as picking pages 4, 6, 8, 5, and 1. therefore, order doesn't matter here, so i use combinations: 10! / (5!5!), not just 10!/5!.
Ron has been teaching various standardized tests for 20 years.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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