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# Set theory and counting and probability

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nojvguiofds

Jul 21, 2018
edited by Max0815  Aug 24, 2018

#1
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Bump....any help?

Jul 21, 2018
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How many distinct subsets of the set S={1,8,9,39,52,91} have odd sums?

Note that we  can choose any of the "odds" for a subset  =  4 subsets

And choosing any two of the elements we need   a set of { even, odd}  to have an  odd sum

We have  2 evens  and they can  be paired with any of the 4 odds..so  2 * 4  =  8 subsets

And choosing any 3  of the elements we need  either

{ even, even, odd}  or  {  odd, odd, odd}  to have an odd sum

In the  first case....we can choose both evens and pair them with each of the 4  odds =  4 subsets

In the second case....we can  choose any 3 of the 4  odds  = 4C3  =  4  subsets

And choosing any  4 of the elements we can have   ( even, odd, odd, odd}

We have 2 evens and again, we can choose  any 3 of 4 odds   = 2  * 4C3 = 2 * 4  = 8

And choosing any  5 of the elements we just need   (even, even, odd, odd, odd}

The two evens will appear in any of these sets by default and, again, we only need to  choose any 3 of 4 odds to  complete the set = 4C3  = 4  subsets

Note that we  cannot take all 6 elements as a sum.....[it would be even...]

So...the total possible subsets = 4 + 8 + 4 + 4 + 8 + 4   =  32 subsets   Jul 21, 2018
edited by CPhill  Jul 21, 2018
edited by CPhill  Jul 21, 2018
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I see, thanks!!!!...also solved both.

Jul 21, 2018
edited by Max0815  Jul 21, 2018