document.write( "Question 530844: How many different 10-letter words (real or imaginary) can be formed from the following letters? IMWOSWMCIA \n" ); document.write( "

Algebra.Com's Answer #350240 by Edwin McCravy(20055) $\"\"$ $\"About$

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document.write( "If it were \r\n" );
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document.write( "IMWOSwmCiA, (where you could tell I from i, M from m, and W from w \r\n" );
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document.write( "it would be 10!\r\n" );
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document.write( "But since we cannot tell the difference between i and I, since they are both\r\n" );
document.write( "capital, we have to divide by 2! so as not to count iMWOSwmCIA and IMWOSwmCiA\r\n" );
document.write( "as two separate arrangements.\r\n" );
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document.write( "So we take out what we consider as I-duplications and we get \r\n" );
document.write( "as the number of arrangements of IMWOSwmCIA.\r\n" );
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document.write( "But since we also cannot tell the difference between m and M, we have to \r\n" );
document.write( "divide by 2! again so as not to count ImWOSwMCIA and IMWOSwmCIA as two \r\n" );
document.write( "separate arrangements.\r\n" );
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document.write( "So we take out what we consider as M-duplications and we get \r\n" );
document.write( "as the number of arrangements of IMWOSwMCIA.\r\n" );
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document.write( "But since we also cannot tell the difference between w and W, we have to\r\n" );
document.write( "divide by 2! again so as not to count IMwOSWMCIA and IMWOSwMCIA as two separate\r\n" );
document.write( "arrangements.\r\n" );
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document.write( "So we take out what we consider as W-duplications and finally we get\r\n" );
document.write( " as the number of arrangements of IMWOSWMCIA.\r\n" );
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document.write( " =  =  = 453600.\r\n" );
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document.write( "And that's the number of distinguishable arrangements of IMWOSWMCIA.\r\n" );
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document.write( "Edwin

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