document.write( "Question 614924: HOW MANY SUBSETS ARE POSSIBLE FROM A SET WITH 55 ELEMENTS? \n" ); document.write( "

Algebra.Com's Answer #386773 by ashipm01(26) $\"\"$ $\"About$

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There are $\"2%5En\"$ subsets of an n element set. So, for n = 55, as in the problem statement, there are $\"2%5E55\"$ , or 36,028,797,018,963,968, subsets.\r
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\n" ); document.write( "\n" ); document.write( "The reason there are $\"2%5En\"$ subsets is because each of the n elements in the set will either be in each subset or it will not be. So for each of the n elements, there are two possible states each one can be in for each subset, and thus there are $\"2%5En\"$ ways of forming subsets from an n element set.\r
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\n" ); document.write( "\n" ); document.write( "Take for example this set of three elements: {1, 2, 3}. Since there are three elements, there are $\"2%5E3+=+8\"$ subsets, shown here.\r
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\n" ); document.write( "\n" ); document.write( "{},
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\n" ); document.write( "\n" ); document.write( "The first subset is the empty set. That is formed by not including any of the elements. Next is just a single element subset formed by including the first element and excluding the other two elements. Each of the remaining subsets is formed in a similar manner, by including some elements and excluding other elements. And for each element, it is either in or out of each subset, so there are $\"2%5En\"$ subsets for any n element set. \n" ); document.write( "

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