document.write( "Question 1117996: Assume there are 5 braille dots (raised and flat) on a given surface. How many letters are possible if at least 1 dot is raised? \n" ); document.write( "

Algebra.Com's Answer #733222 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "As I understand the question, it is not about real letters for blind persons.\r\n" );
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document.write( "It is about abstract \"letters\", that are defined as different combinations of raised dots on a given surface.\r\n" );
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document.write( "The number of different combinations of raised dots is equal to the number of all subsets of the set of 5 elements.\r\n" );
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document.write( "It is well known fact that the number of all subsets of any finite set of N elements is  , incliding\r\n" );
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document.write( "the empty subset and the proper subset.\r\n" );
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document.write( "Since the empty subset is excluded by the condition,  we have for N= 5 given braille dots   = 32-1 = 31  possible non-empty subsets,\r\n" );
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document.write( "and, hence, 31 possible \"abstract\" letters.\r\n" );
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\n" ); document.write( "For discussion and the proof of this formula $\"2%5EN\"$ for the number of subsets of the given finite set of N elements, see the lesson\r
\n" ); document.write( "\n" ); document.write( " - How many subsets are there in a given finite set of n elements?\r
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