document.write( "Question 1180815: Consider the distinct arrangements of the 12 letters in the word PALEOZOOLOGY\r
\n" ); document.write( "\n" ); document.write( "How many distinct arrangements have none of the 5 letters G, L, L, P, Z adjacent?\r
\n" ); document.write( "\n" ); document.write( "I have no idea where to start. Any help is appreciated. \n" ); document.write( "
Algebra.Com's Answer #811095 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "First we'll find all the distinguishable arrangements of AEOOOOY.\r\n" );
document.write( "Then we'll insert the others G,L,L,P,Z among them so that none will be\r\n" );
document.write( "adjacent.\r\n" );
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document.write( "There are 7!/4! = 210 distinguishable arrangements of AEOOOOY.\r\n" );
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document.write( "This could be a sample of those, putting blanks for possible places to\r\n" );
document.write( "insert other letters\r\n" );
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document.write( "_A_E_O_Y_O_O_O_\r\n" );
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document.write( "We can pick any 2 of the 8 blanks to put the 2 L's in C(8,2)=28 ways.\r\n" );
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document.write( "Then we'd have something like this, where the x's are places where the G,P,Z\r\n" );
document.write( "cannot go, next to either L:\r\n" );
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document.write( "_A_ExLxOxLxO_A_O_Y_\r\n" );
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document.write( "So there are P(6,3) = 120 choices of positions for G,P,Z.\r\n" );
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document.write( "Answer: 210*28*120 = 705,600\r\n" );
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document.write( "Edwin
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