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!

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**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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