document.write( "Question 945842: The alphabet contains 26 letters, 5 of them are vowel. How many codes consisting of 5 letters, 3 consonants and 2 vowels can be formed? From this amount, how many are there that \r
\n" ); document.write( "\n" ); document.write( "a) contain the letter b?
\n" ); document.write( "b) contain both the letters b and c?
\n" ); document.write( "c) contain the letter b and end with c? \n" ); document.write( "
Algebra.Com's Answer #576978 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
The alphabet contains 26 letters, 5 of them are vowel. How many codes consisting
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\r\n" );
document.write( "It doesn't say whether letters can be repeated.  I'll assume they\r\n" );
document.write( "cannot be repeated.  [If letters can be repeated tell me in the thank-\r\n" );
document.write( "you note form below and I'll get back to you with that solution.]\r\n" );
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\n" ); document.write( "From this amount, how many are there that
\n" ); document.write( "a) contain the letter b?
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\r\n" );
document.write( "There are 26-5= 21 consonants, including b.\r\n" );
document.write( "Choose \"b\" 1C1 way.\r\n" );
document.write( "There are 20 consonants besides \"b\".\r\n" );
document.write( "Choose the 2 consonants besides \"b\" in 20C2 ways.\r\n" );
document.write( "Choose the 2 vowels 5C2 ways.\r\n" );
document.write( "The 5 letters can be arranged in 5! ways.\r\n" );
document.write( "That's 1C1*20C2*5C2*5! = 1*190*10*120 = 228000 \r\n" );
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\n" ); document.write( "b) contain both the letters b and c?
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document.write( "There are 26-5 consonants, including \"b\" and \"c\".\r\n" );
document.write( "Choose \"b\" 1C1 way.\r\n" );
document.write( "Choose \"c\" 1C1 way,\r\n" );
document.write( "There are 19 consonants besides \"b\" and \"c\".\r\n" );
document.write( "Choose the 1 consonant besides \"b\" and \"c\" in 19C1 ways.\r\n" );
document.write( "Choose the 2 vowels 5C2 ways.\r\n" );
document.write( "The 5 letters can be arranged in 5! ways.\r\n" );
document.write( "That's 1C1*19C1*5C2*5! = 1*19*10*120 = 22800 \r\n" );
document.write( "

\n" ); document.write( "c) contain the letter b and end with c?
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document.write( "There are 26-5 consonants, including \"b\" and \"c\".\r\n" );
document.write( "Choose \"b\" 1C1 way.\r\n" );
document.write( "Choose \"c\" 1C1 way to place at the end.\r\n" );
document.write( "There are 19 consonants besides \"b\" and \"c\".\r\n" );
document.write( "Choose the 1 consonant besides \"b\" and \"c\" in 19C1 ways.\r\n" );
document.write( "Choose the 2 vowels 5C2 ways.\r\n" );
document.write( "The 4 letters other than the \"c\" at the end can be \r\n" );
document.write( "arranged in 4! ways.\r\n" );
document.write( "That's 1C1*19C1*5C2*4! = 1*19*10*24 = 4560  \r\n" );
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document.write( "Edwin
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