Posted by Eleanor on Thursday, February 19, 2009 at 6:28pm.
Assume that the set S has 10 elements.
How many subsets of S have at most 4 elements?
This question is from the section in my book called "Counting Partitions: Combinations." I would greatly appreciate any help! Thanks!

Math  drwls, Thursday, February 19, 2009 at 7:19pm
It seems to me there are 10 ways to pick subsets of 1 element; 10!/(8! 2!)= 45 subsets with 2 elements; 10!/(7!3!) = 120 with three elements and 10!/(6!4!) = 210 subsets with four elements
The total is 385.

Math  Eleanor, Thursday, February 19, 2009 at 8:29pm
Hey, thanks! However, that answer was not right. Any other ideas? You seem to be on the right track... This problem really confuses me.

Math  Eleanor, Thursday, February 19, 2009 at 9:37pm
Ok, the answer is 386! Yay! However, I am not sure why the answer is not 385.... maybe because we had to add c(10,0) into the mix. Thanks so much for the help... I wouldn't have gotten the answer had it not been for your help!
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