document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1036011>Question 1036011</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve just two more questions PLease. Thank you.<BR>\n" );
document.write( "1.Eight students are on standby to fly back to school<BR>\n" );
document.write( "at the end of spring break. The airline finds it has<BR>\n" );
document.write( "space for three of them. How many ways can the<BR>\n" );
document.write( "three be selected ignoring who were first to arrive<BR>\n" );
document.write( "at the terminal?\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
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document.write( "2.An ATM keypad has ten keys. A PIN code is entered<BR>\n" );
document.write( "by pressing a sequence of four keys.<BR>\n" );
document.write( "(a) How many PIN codes are possible if no key is<BR>\n" );
document.write( "pressed twice in a code?<BR>\n" );
document.write( "(b) How many PIN codes are<BR>\n" );
document.write( "possible if a key may be<BR>\n" );
document.write( "pressed more than once in<BR>\n" );
document.write( "a code?<BR>\n" );
document.write( "(c) A bank changes the PIN<BR>\n" );
document.write( "codes to a sequence of six<BR>\n" );
document.write( "keys. Find the number of<BR>\n" );
document.write( "PIN codes possible if a key<BR>\n" );
document.write( "may be pressed more than<BR>\n" );
document.write( "once in a sequence. Discuss the increase in security<BR>\n" );
document.write( "by going to a six-key code. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #650640 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=650640\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.Eight students are on standby to fly back to school<BR>\n" );
document.write( "at the end of spring break. The airline finds it has<BR>\n" );
document.write( "space for three of them. How many ways can the<BR>\n" );
document.write( "three be selected ignoring who were first to arrive<BR>\n" );
document.write( "at the terminal?<BR>\n" );
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document.write( "Ans: 8C3 = (8*7*6)/(1*2*3) = 8*7 = 56 ways<BR>\n" );
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document.write( "2.An ATM keypad has ten keys. A PIN code is entered<BR>\n" );
document.write( "by pressing a sequence of four keys.<BR>\n" );
document.write( "(a) How many PIN codes are possible if no key is<BR>\n" );
document.write( "pressed twice in a code?<BR>\n" );
document.write( "Ans: 10*9*8*7 = 5040<BR>\n" );
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document.write( "(b) How many PIN codes are<BR>\n" );
document.write( "possible if a key may be<BR>\n" );
document.write( "pressed more than once in<BR>\n" );
document.write( "a code?<BR>\n" );
document.write( "Ans: 10^4 = 10000<BR>\n" );
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document.write( "(c) A bank changes the PIN<BR>\n" );
document.write( "codes to a sequence of six<BR>\n" );
document.write( "keys. Find the number of<BR>\n" );
document.write( "PIN codes possible if a key<BR>\n" );
document.write( "may be pressed more than<BR>\n" );
document.write( "once in a sequence. Discuss the increase in security<BR>\n" );
document.write( "by going to a six-key code.<BR>\n" );
document.write( "Ans: 10^6 = 1000000 ways<BR>\n" );
document.write( "----<BR>\n" );
document.write( "The 6 key code is 100 times more secure as the 4 key code.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "-------------- </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );