document.write( "Question 614924: HOW MANY SUBSETS ARE POSSIBLE FROM A SET WITH 55 ELEMENTS? \n" ); document.write( "
Algebra.Com's Answer #386778 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
how many subsets are possible in a set with 3 elements.
\n" ); document.write( "let's see.
\n" ); document.write( "suppose the elements are a,b,c
\n" ); document.write( "you can have:
\n" ); document.write( "abc
\n" ); document.write( "ab
\n" ); document.write( "ac
\n" ); document.write( "bc
\n" ); document.write( "a
\n" ); document.write( "b
\n" ); document.write( "c
\n" ); document.write( "how many subsets are possible in a set with 4 elements.
\n" ); document.write( "let's see.
\n" ); document.write( "suppose the elements are a,b,c,d
\n" ); document.write( "you can have:
\n" ); document.write( "abcd
\n" ); document.write( "abc
\n" ); document.write( "abd
\n" ); document.write( "acd
\n" ); document.write( "bcd
\n" ); document.write( "ab
\n" ); document.write( "ac
\n" ); document.write( "ad
\n" ); document.write( "bc
\n" ); document.write( "bd
\n" ); document.write( "cd
\n" ); document.write( "a
\n" ); document.write( "b
\n" ); document.write( "c
\n" ); document.write( "d
\n" ); document.write( "we don't count the null set (no elements in it).
\n" ); document.write( "the number of subsets when you have 3 elements becomes:
\n" ); document.write( "3c1 + 3c2 + cc3
\n" ); document.write( "the number of subsets when you have 4 elements becomes:
\n" ); document.write( "4c1 + 4c2 + 4c3 + 4c4
\n" ); document.write( "the number of subsets when you have 55 elements becomes:
\n" ); document.write( "55c1 + 55c2 + 55c3 + ......... + 55c54 + 55c55
\n" ); document.write( "that's a big number.
\n" ); document.write( "i used excel to calculate it.
\n" ); document.write( "here's the results:
\n" ); document.write( "
\r\n" );
document.write( "	total >>>>>>>>>>>>	3.60288E+16\r\n" );
document.write( "n	x	ncx\r\n" );
document.write( "55	1	55\r\n" );
document.write( "55	2	1485\r\n" );
document.write( "55	3	26235\r\n" );
document.write( "55	4	341055\r\n" );
document.write( "55	5	3478761\r\n" );
document.write( "55	6	28989675\r\n" );
document.write( "55	7	202927725\r\n" );
document.write( "55	8	1217566350\r\n" );
document.write( "55	9	6358402050\r\n" );
document.write( "55	10	29248649430\r\n" );
document.write( "55	11	1.19654E+11\r\n" );
document.write( "55	12	4.3873E+11\r\n" );
document.write( "55	13	1.45118E+12\r\n" );
document.write( "55	14	4.35355E+12\r\n" );
document.write( "55	15	1.18997E+13\r\n" );
document.write( "55	16	2.97493E+13\r\n" );
document.write( "55	17	6.82483E+13\r\n" );
document.write( "55	18	1.4408E+14\r\n" );
document.write( "55	19	2.80576E+14\r\n" );
document.write( "55	20	5.05037E+14\r\n" );
document.write( "55	21	8.41729E+14\r\n" );
document.write( "55	22	1.30085E+15\r\n" );
document.write( "55	23	1.86644E+15\r\n" );
document.write( "55	24	2.48859E+15\r\n" );
document.write( "55	25	3.08585E+15\r\n" );
document.write( "55	26	3.5606E+15\r\n" );
document.write( "55	27	3.82435E+15\r\n" );
document.write( "55	28	3.82435E+15\r\n" );
document.write( "55	29	3.5606E+15\r\n" );
document.write( "55	30	3.08585E+15\r\n" );
document.write( "55	31	2.48859E+15\r\n" );
document.write( "55	32	1.86644E+15\r\n" );
document.write( "55	33	1.30085E+15\r\n" );
document.write( "55	34	8.41729E+14\r\n" );
document.write( "55	35	5.05037E+14\r\n" );
document.write( "55	36	2.80576E+14\r\n" );
document.write( "55	37	1.4408E+14\r\n" );
document.write( "55	38	6.82483E+13\r\n" );
document.write( "55	39	2.97493E+13\r\n" );
document.write( "55	40	1.18997E+13\r\n" );
document.write( "55	41	4.35355E+12\r\n" );
document.write( "55	42	1.45118E+12\r\n" );
document.write( "55	43	4.3873E+11\r\n" );
document.write( "55	44	1.19654E+11\r\n" );
document.write( "55	45	29248649430\r\n" );
document.write( "55	46	6358402050\r\n" );
document.write( "55	47	1217566350\r\n" );
document.write( "55	48	202927725\r\n" );
document.write( "55	49	28989675\r\n" );
document.write( "55	50	3478761\r\n" );
document.write( "55	51	341055\r\n" );
document.write( "55	52	26235\r\n" );
document.write( "55	53	1485\r\n" );
document.write( "55	54	55\r\n" );
document.write( "55	55	1\r\n" );
document.write( "

\n" ); document.write( "the total number of possible subsets looks like it's 3.60288 * 10^16.
\n" ); document.write( "Each one of the subsets is unique in that it contains at least 1 element in it that's unique from any other subset with the same number of elements in it.
\n" ); document.write( "i won't swear that this is correct, but it's based on a reasonable assumption.
\n" ); document.write( "look at the set with 3 elements in it and you'll see that each of the subsets is unique.
\n" ); document.write( "the subset with 3 elements in it is abc which is the set itself.
\n" ); document.write( "every set is a subset of itself.
\n" ); document.write( "the subsets with 2 elements in them are unique.
\n" ); document.write( "they contain:
\n" ); document.write( "ab
\n" ); document.write( "ac
\n" ); document.write( "bc
\n" ); document.write( "the subsets with 1 element in them are unique.
\n" ); document.write( "they contain:
\n" ); document.write( "a
\n" ); document.write( "b
\n" ); document.write( "c
\n" ); document.write( "we cover all of the subsets by including all subsets that have 1 less element in them then the previous set of subsets.
\n" ); document.write( "this is my guess.
\n" ); document.write( "like i say, i won't swear to it, but i think it's a reasonable assumption.
\n" ); document.write( "without any precedence to guide me, i'd say this is my best guess.
\n" ); document.write( "there are intersections with the other subsets.
\n" ); document.write( "for example:
\n" ); document.write( "the set ab and the set ac have a common element of a.
\n" ); document.write( "the set ac and the set bc have a common element of c.
\n" ); document.write( "this is to be expected.
\n" ); document.write( "they are still unique subsets because they each have an element in them that is not in the other set.\r
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