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document.write( "There are four types of words that can be made from the letters of TOMORROW.\r\n" );
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document.write( "Type 1: ABCD (4 distinguishable letters) each of which can be arranged in \r\n" );
document.write( " 4!= 24 ways; \r\n" );
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document.write( "Type 2: AABB (2 pairs of indistinguishable letters) each of which can be\r\n" );
document.write( " arranged in 4!/(2!2!) = 6 ways;\r\n" );
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document.write( "Type 3: AAAB (3 indistinguishable letters and 1 different letter, which can be\r\n" );
document.write( " arranged in 4!/3! = 4 ways.\r\n" );
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document.write( "Type 4: AABC (2 indistinguishable letters and 2 other distinguishable letters,\r\n" );
document.write( " each of which can be arranged in 4!/2! = 12 ways\r\n" );
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document.write( "Put these into cases:\r\n" );
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document.write( "Case 1: The ABCD-type words. \r\n" );
document.write( " Choose 4 letters from {M,O,R,T,W} in 5C4 = 5 ways.\r\n" );
document.write( " From the above, each can be arranged in 24 ways.\r\n" );
document.write( " That's 5∙24=120 ways.\r\n" );
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document.write( "Case 2: The AABB-type words.\r\n" );
document.write( " These are the arrangements of OORR\r\n" );
document.write( " From the above, there are 6 of these.\r\n" );
document.write( " That's 6 ways for case 2. \r\n" );
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document.write( "Case 3. The AAAB-type words.\r\n" );
document.write( " The three indistinguishable letters can only be O's.\r\n" );
document.write( " The letter of which there is only 1 is chosen from {M,R,T,W}, 4 ways.\r\n" );
document.write( " There are 4 ways to choose the other letter.\r\n" );
document.write( " From the above, each can be arranged in 4 ways.\r\n" );
document.write( " That's 4∙4=16 ways \r\n" );
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document.write( "Case 4. The AABC-type words.\r\n" );
document.write( " Choose the letter for the two indistinguishable letters 2 ways (O or R)\r\n" );
document.write( " Choose the two distinguishable letters from the other 4 letters in\r\n" );
document.write( " 4C2=6 ways\r\n" );
document.write( " From the above, each can be arranged in 12 ways\r\n" );
document.write( " That's 2∙6∙12 = 144 ways \r\n" );
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document.write( "Answer: 120+6+16+144 = 286 four-letter words.\r\n" );
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document.write( "Edwin \n" );
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