document.write( "Question 1191221: 7. How many signals can be made with 5 different flags by raising them any number at a time?\r
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Algebra.Com's Answer #823016 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "How many signals can be made with 5 different flags by raising them any number at a time?
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\n" ); document.write( "\n" ); document.write( "            As worded, this problem admits different readings, interpretations, solutions and answers.\r
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\n" ); document.write( "\n" ); document.write( "            See my interpretation, different from that of the other tutor.\r
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\n" ); document.write( "\n" ); document.write( "            I will assume that 5 flags are NOT ONLY DIFFERENT (they always are different), but distinguished.\r
\n" ); document.write( "\n" ); document.write( "            More concretely and for clarity, I will assume that the flags have different colors.\r
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document.write( "By raising one flag at a time, I can make 5 different signals.\r\n" );
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document.write( "By raising two flags at a time, I can make 5*4 = 20 different signals \r\n" );
document.write( "    (if to read them from top to bottom, or from left to right).\r\n" );
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document.write( "By raising three flags at a time, I can make 5*4*3 = 60 different signals \r\n" );
document.write( "    (if to read them from top to bottom, or from left to right).\r\n" );
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document.write( "By raising four flags at a time, I can make 5*4*3*2 = 120 different signals \r\n" );
document.write( "    (if to read them from top to bottom, or from left to right).\r\n" );
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document.write( "By raising five flags at a time, I can make 5*4*3*2*1 = 120 different signals \r\n" );
document.write( "    (if to read them from top to bottom, or from left to right).\r\n" );
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document.write( "In all, I can make  5 + 20 + 60 + 120 + 120 = 325 different signals,\r\n" );
document.write( "    by raising different number of distinguishable flags at a time.\r\n" );
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