Question 614924
There are {{{2^n}}} subsets of an n element set. So, for n = 55, as in the problem statement, there are {{{2^55}}}, or 36,028,797,018,963,968, subsets.


The reason there are {{{2^n}}} 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^n}}} ways of forming subsets from an n element set.


Take for example this set of three elements:  {1, 2, 3}. Since there are three elements, there are {{{2^3 = 8}}} subsets, shown here.


{},
{1},
{2},
{3},
{1,2},
{1,3},
{2,3},
{1,2,3}


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^n}}} subsets for any n element set.