document.write( "Question 459567: How many strings of five upper class English letters are there for each of the following restrictions?
\n" ); document.write( "A string of letters need not be a real word, so XYZWT is a good string.\r
\n" ); document.write( "\n" ); document.write( "a. Start with an X and letters can be repeated\r
\n" ); document.write( "\n" ); document.write( "b. No letter can be repeated\r
\n" ); document.write( "\n" ); document.write( "c. Start and end with an X and letters can be repeated\r
\n" ); document.write( "\n" ); document.write( "d. Start with the letters BO(in that order) and letters can be repeated \r
\n" ); document.write( "\n" ); document.write( "e. Start and end with the letters BO(in that order) and letters can be repeated\r
\n" ); document.write( "\n" ); document.write( "f. Start or end with the letters BO(in that order)if letters can be repeated \n" ); document.write( "
Algebra.Com's Answer #315185 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
a. Start with an X and letters can be repeated
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document.write( "Examples:  XAJQN, XLLTX, XXXXX \r\n" );
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document.write( "Choose letter#1 1 way, choose letter#2 26 ways, \r\n" );
document.write( "choose letter#3 26 ways, choose letter#4 26 ways,\r\n" );
document.write( "choose letter#5 26 ways.\r\n" );
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document.write( "That's 1×26×26×26×26 = 456976 ways\r\n" );
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\n" ); document.write( "b. No letter can be repeated
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document.write( "Examples:  kYUDM, PIANO, VWXYZ\r\n" );
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document.write( "Choose letter#1 26 ways, choose letter#2 25 ways, \r\n" );
document.write( "choose letter#3 24 ways, choose letter#4 23 ways,\r\n" );
document.write( "choose letter#5 22 ways.\r\n" );
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document.write( "That's 26×25×24×23×22 = 7893600 ways.\r\n" );
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\n" ); document.write( "c. Start and end with an X and letters can be repeated
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document.write( "Examples:  XEROX, XFFJX, XXXXX\r\n" );
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document.write( "Choose letter#1 1 way, choose letter#2 26 ways, \r\n" );
document.write( "choose letter#3 26 ways, choose letter#4 26 ways,\r\n" );
document.write( "choose letter#5 1 way.\r\n" );
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document.write( "That's 1×26×26×26×1 = 17576 ways.\r\n" );
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\n" ); document.write( "d. Start with the letters BO(in that order) and letters can be repeated
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document.write( "Examples:  BOOZE, BOAST, BOBOO\r\n" );
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document.write( "Choose letter#1 1 way, choose letter#2 1 way, \r\n" );
document.write( "choose letter#3 26 ways, choose letter#4 26 ways,\r\n" );
document.write( "choose letter#5 26 ways.\r\n" );
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document.write( "That's 1×1×26×26×26 = 17576 ways.\r\n" );
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document.write( "---------------------------------\r\n" );
document.write( "

\n" ); document.write( "e. Start and end with the letters BO(in that order) and letters can be repeated
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document.write( "Examples:  BOOBO, BOMBO, BOBBO\r\n" );
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document.write( "Choose letter#1 1 way, choose letter#2 1 way, \r\n" );
document.write( "choose letter#3 26 ways, choose letter#4 1 way,\r\n" );
document.write( "choose letter#5 1 ways.\r\n" );
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document.write( "That's 1×1×26×1×1 = 26 ways.\r\n" );
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document.write( "

\n" ); document.write( "f. Start or end with the letters BO(in that order)if letters can be repeated
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document.write( "We must use a formula here:\r\n" );
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document.write( "N(X or Y) = N(X) + N(Y) - N(X and Y), \r\n" );
document.write( "  where N( ) means \"the number of\".\r\n" );
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document.write( "Let X be \"words beginning with BO\", \r\n" );
document.write( "        calculated in part d, so N(X) = 17576\r\n" );
document.write( "Let Y be \"words ending with BO\", \r\n" );
document.write( "        same as the results of part d, so N(Y) = 17576\r\n" );
document.write( "Then \"X and Y\" will be \"words beginning \r\n" );
document.write( "        and ending with BO\", calculated \r\n" );
document.write( "        in part e, so N(X and Y) = 26\r\n" );
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document.write( "N(X or Y) = 17576 + 17576 - 26 = 35126\r\n" );
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document.write( "Edwin

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