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How many subsets containing an odd number of elements does a set with 10 elements have?
Wiki User
∙ 11y ago
We are looking for all sets with an odd number of elements in them. To find this we can use combinations. Adding up the odd combinations will total the subsets containing an odd number of elements.nCr where n=10 and r=(1,3,5,7,9)
10C1 + 10C3 + 10C5 + 10C7 + 10C9 = 512.
You could also take the total number of elements (2^10) and subtract all sets containing an even number of elements.
nCr where n=10 and r=(0,2,4,6,8,10)
1024-(1+45+210+210+45+1)=512
Wiki User
∙ 11y ago
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