document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=304515>Question 304515</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the ordinary alphabet of 26-letters.\r<BR>\n" );
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document.write( "a) Define a \"4-letter word\" to be any list of 4 letters that contains at least one of the vowels A, E, I, O, U. How many 4-letter words are there?\r<BR>\n" );
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document.write( "b) Suppose, instead, we define a \"4-letter word\" to be any list of 4 letters that contains exactly one of the vowels A, E, I, O, U. How many 4-letter words are there? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218031 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=218031\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the ordinary alphabet of 26-letters. <BR>\n" );
document.write( "a) Define a \"4-letter word\" to be any list of 4 letters that contains at least one of the vowels A, E, I, O, U. How many 4-letter words are there?<BR>\n" );
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document.write( "Assuming that repetition is not allowed:\r<BR>\n" );
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document.write( "There are 26*25*24*23 4-letter words with no restrictions.<BR>\n" );
document.write( "There are 19*18*17*16 4-letter words that have no vowels.<BR>\n" );
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document.write( "So, there are (26*25*24*23)-(19*18*17*16) 4-letter words that have at least one vowel.<BR>\n" );
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document.write( "b) Suppose, instead, we define a \"4-letter word\" to be any list of 4 letters that contains exactly one of the vowels A, E, I, O, U. How many 4-letter words are there?<BR>\n" );
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document.write( "5-ways to choose the vowel<BR>\n" );
document.write( "19*18*17 ways to choose the other three letters<BR>\n" );
document.write( "Total words = 5*19*18*17<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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