document.write( "Question 1175422: Find the number of ways of arranging all 12 letters of word STRAWBERRIES where
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Algebra.Com's Answer #801058 by Edwin McCravy(20055)\"\" \"About 
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Find the number of ways of arranging all 12 letters of word STRAWBERRIES where
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document.write( "To make things easier, put the letters of STRAWBERRIES in alphabetical order:\r\n" );
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document.write( "A,B,E,E,I,R,R,R,T,S,S,W\r\n" );
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document.write( "The vowels are A,E,E,I\r\n" );
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document.write( "Case 1. No E's on either end. A and I are on the ends.  \r\n" );
document.write( "That's 2!=2 ways they can go on the two ends.\r\n" );
document.write( "Between them are the distinguishable 10-letter arrangements of \r\n" );
document.write( "B,E,E,R,R,R,T,S,S,W or 10!/(2!3!2!) \r\n" );
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document.write( "That's 2![10!/(2!3!2!)] = 302400 ways for Case 1.\r\n" );
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document.write( "Case 2. Exactly 1 E on one end. That puts A or I on the opposite end.\r\n" );
document.write( "Choose the end (left or right) to put the E on in 2 ways.\r\n" );
document.write( "That's 2! ways to place the E\r\n" );
document.write( "Choose letter A or I to put on the opposite end in 2 ways.\r\n" );
document.write( "That's 2!(2) ways to put the vowels on the ends, exactly one being an E.\r\n" );
document.write( "Between the vowels on the ends are the distinguishable 10-letter arrangements\r\n" );
document.write( "of X,B,E,R,R,R,T,S,S,W, or 10!/(3!2!), where the X represents A or I, the one\r\n" );
document.write( "not chosen for the opposite end.\r\n" );
document.write( "or 10!/(3!2!)  \r\n" );
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document.write( "That's (2!)(2)[10!/(3!2!)] = 1209600 ways for Case 2.\r\n" );
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document.write( "Case 3. E's on both ends.  \r\n" );
document.write( "Between them are the distinguishable 10-letter arrangements of\r\n" );
document.write( "A,B,I,R,R,R,T,S,S,W or 10!/(3!2!) = 302400 for case 3.\r\n" );
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document.write( "For all three cases, that's 302400+1209600+302400 = 1814400 ways.  \r\n" );
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document.write( "Edwin
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