document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=197539>Question 197539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a) Using the letters in the word \"OCTAGON,\" how many distinct arrangements using all 7 letters are possible?<BR>\n" );
document.write( "b) Using the letters in the word \"TRAPEZOID,\" how many distinct combinations using 7 letters at a time are possible?<BR>\n" );
document.write( "c) Using the letters in the word \"SQUARE,\" what is the probability that a 6-letter arrangement the first 2 letters are vowels?<BR>\n" );
document.write( "d) Using the letters in the word \"RHOMBUS,\" what is probability that in a 7-letter arrangement the first 3 letters are vowels? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #148156 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=148156\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a) Using the letters in the word \"OCTAGON,\" how many distinct arrangements using all 7 letters are possible?<BR>\n" );
document.write( "Ans: 7!/2! = 2520<BR>\n" );
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document.write( "b) Using the letters in the word \"TRAPEZOID,\" how many distinct combinations using 7 letters at a time are possible?<BR>\n" );
document.write( "Ans: 9P7 = 9!/(9-7)! = 9!/2! = 181440<BR>\n" );
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document.write( "c) Using the letters in the word \"SQUARE,\" what is the probability that a 6-letter arrangement the first 2 letters are vowels?<BR>\n" );
document.write( "# of ways to pick the two vowels: 3C2 = 3<BR>\n" );
document.write( "# of ways to arrange those two vowels = 2<BR>\n" );
document.write( "# of ways to arrange the rest of the letters = 4! = 24<BR>\n" );
document.write( "# of ways to arrange the 6 letters with no special restrictions: 6!<BR>\n" );
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document.write( "Ans: Probability of satisfying the condition = [3*2*24]/6! = 0.2<BR>\n" );
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document.write( "d) Using the letters in the word \"RHOMBUS,\" what is probability that in a 7-letter arrangement the first 3 letters are vowels?<BR>\n" );
document.write( "Pick three vowels: 0 ways because there are not three vowels in RHOMBUS.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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