document.write( "Question 1156752: How many ways can you arrange the letters of the word MAMMALIA provided no vowels are put together. \n" ); document.write( "
Algebra.Com's Answer #779535 by Edwin McCravy(20056) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "I'm afraid the other tutor's solution is incorrect.  But we're just human, and\r\n" );
document.write( "all of us mess up sometimes.  I've messed up a number of times!\r\n" );
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document.write( "MAMMALIA\r\n" );
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document.write( "The vowels are A,A,I, and A.\r\n" );
document.write( "The consonants are M,M,M, and L.\r\n" );
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document.write( "There are only 5 basic ways we can arrange them, vowel and consonant-wise \r\n" );
document.write( "so that no vowels are put together:\r\n" );
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document.write( "CVCVCVCV, VCVCVCVC, VCCVCVCV, VCVCCVCV, VCVCVCCV\r\n" );
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document.write( "There are 4 vowels, among which 3 A's are indistinguishable.\r\n" );
document.write( "There are 4 consonants, among which 3 M's are indistinguishable.\r\n" );
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document.write( "So for each of those 5 there are 4!/3!=4 distinguishable ways to place the 4 vowels.\r\n" );
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document.write( "And there are 4!/3!=4 distinguishable ways to place the 4 consonants.\r\n" );
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document.write( "So there are 5*4*4=80 ways to place them.  Here are all 80, generated\r\n" );
document.write( "by a computer program in alphabetical order.  It's fun trying to pronounce\r\n" );
document.write( "them. My favorite is Number 73, MAMALIMA. If your MAMA was a LIMA, you'd be\r\n" );
document.write( "a son of a bean. lol\r\n" );
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document.write( " 1.  ALAMAMIM\r\n" );
document.write( " 2.  ALAMAMMI\r\n" );
document.write( " 3.  ALAMIMAM\r\n" );
document.write( " 4.  ALAMIMMA\r\n" );
document.write( " 5.  ALAMMAMI\r\n" );
document.write( " 6.  ALAMMIMA\r\n" );
document.write( " 7.  ALIMAMAM\r\n" );
document.write( " 8.  ALIMAMMA\r\n" );
document.write( " 9.  ALIMMAMA\r\n" );
document.write( "10.  ALMAMAMI\r\n" );
document.write( "11.  ALMAMIMA\r\n" );
document.write( "12.  ALMIMAMA\r\n" );
document.write( "13.  AMALAMIM\r\n" );
document.write( "14.  AMALAMMI\r\n" );
document.write( "15.  AMALIMAM\r\n" );
document.write( "16.  AMALIMMA\r\n" );
document.write( "17.  AMALMAMI\r\n" );
document.write( "18.  AMALMIMA\r\n" );
document.write( "19.  AMAMALIM\r\n" );
document.write( "20.  AMAMALMI\r\n" );
document.write( "21.  AMAMAMIL\r\n" );
document.write( "22.  AMAMAMLI\r\n" );
document.write( "23.  AMAMILAM\r\n" );
document.write( "24.  AMAMILMA\r\n" );
document.write( "25.  AMAMIMAL\r\n" );
document.write( "26.  AMAMIMLA\r\n" );
document.write( "27.  AMAMLAMI\r\n" );
document.write( "28.  AMAMLIMA\r\n" );
document.write( "29.  AMAMMALI\r\n" );
document.write( "30.  AMAMMILA\r\n" );
document.write( "31.  AMILAMAM\r\n" );
document.write( "32.  AMILAMMA\r\n" );
document.write( "33.  AMILMAMA\r\n" );
document.write( "34.  AMIMALAM\r\n" );
document.write( "35.  AMIMALMA\r\n" );
document.write( "36.  AMIMAMAL\r\n" );
document.write( "37.  AMIMAMLA\r\n" );
document.write( "38.  AMIMLAMA\r\n" );
document.write( "39.  AMIMMALA\r\n" );
document.write( "40.  AMLAMAMI\r\n" );
document.write( "41.  AMLAMIMA\r\n" );
document.write( "42.  AMLIMAMA\r\n" );
document.write( "43.  AMMALAMI\r\n" );
document.write( "44.  AMMALIMA\r\n" );
document.write( "45.  AMMAMALI\r\n" );
document.write( "46.  AMMAMILA\r\n" );
document.write( "47.  AMMILAMA\r\n" );
document.write( "48.  AMMIMALA\r\n" );
document.write( "49.  ILAMAMAM\r\n" );
document.write( "50.  ILAMAMMA\r\n" );
document.write( "51.  ILAMMAMA\r\n" );
document.write( "52.  ILMAMAMA\r\n" );
document.write( "53.  IMALAMAM\r\n" );
document.write( "54.  IMALAMMA\r\n" );
document.write( "55.  IMALMAMA\r\n" );
document.write( "56.  IMAMALAM\r\n" );
document.write( "57.  IMAMALMA\r\n" );
document.write( "58.  IMAMAMAL\r\n" );
document.write( "59.  IMAMAMLA\r\n" );
document.write( "60.  IMAMLAMA\r\n" );
document.write( "61.  IMAMMALA\r\n" );
document.write( "62.  IMLAMAMA\r\n" );
document.write( "63.  IMMALAMA\r\n" );
document.write( "64.  IMMAMALA\r\n" );
document.write( "65.  LAMAMAMI\r\n" );
document.write( "66.  LAMAMIMA\r\n" );
document.write( "67.  LAMIMAMA\r\n" );
document.write( "68.  LIMAMAMA\r\n" );
document.write( "69.  MALAMAMI\r\n" );
document.write( "70.  MALAMIMA\r\n" );
document.write( "71.  MALIMAMA\r\n" );
document.write( "72.  MAMALAMI\r\n" );
document.write( "73.  MAMALIMA\r\n" );
document.write( "74.  MAMAMALI\r\n" );
document.write( "75.  MAMAMILA\r\n" );
document.write( "76.  MAMILAMA\r\n" );
document.write( "77.  MAMIMALA\r\n" );
document.write( "78.  MILAMAMA\r\n" );
document.write( "79.  MIMALAMA\r\n" );
document.write( "80.  MIMAMALA\r\n" );
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document.write( "Edwin
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