How many 4 element subsets can you get from a 21 element set. I know the combination formula C(21,4)=5985. I was trying to see how this is working out though. I know there are 2^21 subsets of a 21 element set, I want to know how I can find the number of all the 4 element subsets without using the formula C(n,r).(adsbygoogle = window.adsbygoogle || []).push({});

The way to get 2^21 is to just go down the line for each element in the set. for each element there are 2 choices. Yes or no, so by the multiplication principle you have 2^21 choices. How can I then eliminate all the subsets that have a cardinality other than 4?

Or if there is a better way to than the total minus the bad method that will work I would like to hear that way too.

Thanks for helping....

Jeremy

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# Homework Help: Combinations and subset help

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