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" );
document.write( "\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?\r<BR>\n" );
document.write( "\n" );
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 #218029 by </B><A HREF=/tutors/aboutme.mpl?userid=vleith><B>vleith(2983)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=vleith><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=218029\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assume a four letter word<BR>\n" );
document.write( "If the first letter is a vowel, then it can be 1 of 5 possible letters.<BR>\n" );
document.write( "The remaining 3 letters in the word can be any of 26 letters. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A+26+%2A+26+%2A+26 ALIGN=MIDDLE  ALT=\"5%2A+26+%2A+26+%2A+26\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the first letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26%2A+5+%2A+26+%2A+26 ALIGN=MIDDLE  ALT=\"26%2A+5+%2A+26+%2A+26\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the second letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26+%2A+26+%2A+5+%2A+26 ALIGN=MIDDLE  ALT=\"26+%2A+26+%2A+5+%2A+26\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the third letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=26+%2A+26+%2A+26+%2A+5 ALIGN=MIDDLE  ALT=\"26+%2A+26+%2A+26+%2A+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the fourth letter as a vowel.<BR>\n" );
document.write( "The total would be thge sum of those four products.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "B)<BR>\n" );
document.write( "Part B is a misleading question. Does it mean there is a single vowel in the word or does it mean that multiple occurrences of the same vowel is allowed?<BR>\n" );
document.write( "If a single vowel only is allowed then<BR>\n" );
document.write( "If the first letter is a vowel, then it can be 1 of 5 possible letters.<BR>\n" );
document.write( "The remaining 3 letters in the word can be any consonant letters. So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2A+21+%2A+21+%2A+21 ALIGN=MIDDLE  ALT=\"5%2A+21+%2A+21+%2A+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the first letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21%2A+5+%2A+21+%2A+21 ALIGN=MIDDLE  ALT=\"21%2A+5+%2A+21+%2A+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the second letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+%2A+21+%2A+5+%2A+21 ALIGN=MIDDLE  ALT=\"21+%2A+21+%2A+5+%2A+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the third letter as a vowel.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+%2A+21+%2A+21+%2A+5 ALIGN=MIDDLE  ALT=\"21+%2A+21+%2A+21+%2A+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > gives a word with the fourth letter as a vowel.<BR>\n" );
document.write( "The total would be thge sum of those four products.\r<BR>\n" );
document.write( "\n" );
document.write( "If you are allowed multiple occurrences of the same vowel, then change the 21 above to 22 (since you can have the same vowel again)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );