document.write( "Question 1150911: The English alphabet has 26 letters of which 5 are vowels. Consider only 5-
\n" ); document.write( "letter “words” consisting of 3 different consonants and 2 different vowels. Find
\n" ); document.write( "the number of such words which:
\n" ); document.write( "(a) have no restrictions;
\n" ); document.write( "(c) contain the letters B and C;
\n" ); document.write( "(b) contain the letter B;
\n" ); document.write( "(d) begin with B and contain the letter C. \n" ); document.write( "

Algebra.Com's Answer #772504 by Edwin McCravy(20056) $\"\"$ $\"About$

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The English alphabet has 26 letters of which 5 are vowels. Consider only 5-
\n" ); document.write( "letter “words” consisting of 3 different consonants and 2 different vowels. Find
\n" ); document.write( "the number of such words which:
\n" ); document.write( "(a) have no restrictions;

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document.write( "Choose the three consonants 21C3=1330 ways\r\n" );
document.write( "Choose the two vowels 5C2=10 ways\r\n" );
document.write( "Permute each in 5P5=5!=120 ways\r\n" );
document.write( "That's 1330∙120=1596000 ways\r\n" );
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document.write( "Choose the third consonants 19C1=19 ways\r\n" );
document.write( "Choose the two vowels 5C2=10 ways\r\n" );
document.write( "Permute each in 5P5=5!=120 ways\r\n" );
document.write( "That's 19∙10∙120=22800 ways\r\n" );
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(b) contain the letter B;

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document.write( "Choose the remaining 2 consonants 20C2=190 ways\r\n" );
document.write( "Choose the two vowels 5C2=10 ways\r\n" );
document.write( "Permute each in 5P5=5!=120 ways\r\n" );
document.write( "That's 190∙10∙120=228000 ways\r\n" );
document.write( "

(d) begin with B and contain the letter C.

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document.write( "Choose the other consonant in 19C1=19 ways.\r\n" );
document.write( "Choose the two vowels in 5C2=10 ways.\r\n" );
document.write( "Permute the 4 letters on the right of the B in 4P4=4!=24 ways.\r\n" );
document.write( "That's 19∙10∙24=4560 ways.\r\n" );
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document.write( "Edwin

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