document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083597>Question 1083597</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a computer store receives a shipment of 24 monitors, including 5 defective and 19 good monitors. Three monitors are chosen at random.\r<BR>\n" );
document.write( "\n" );
document.write( "How many selections of 3 are possible?<BR>\n" );
document.write( "How many selections will contain NO defective monitors out of 3? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697600 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=697600\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=\"black\" face=\"times\" size=\"4\">Problem: <BR>\n" );
document.write( "<font color=blue>A computer store receives a shipment of 24 monitors, including 5 defective and 19 good monitors. Three monitors are chosen at random.</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Questions:<BR>\n" );
document.write( "<font color=blue>Part A) How many selections of 3 are possible?<BR>\n" );
document.write( "Part B) How many selections will contain NO defective monitors out of 3?</font>\r<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------------------------<BR>\n" );
document.write( "-----------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answers:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Answer for part A): <font color=red>2024</font><BR>\n" );
document.write( "Answer for part B): <font color=red>969</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "-----------------------------------------------------------------------------<BR>\n" );
document.write( "-----------------------------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Explanation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part A)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have 24 monintors total. The pool size is n = 24. <BR>\n" );
document.write( "When I use the term \"pool\", I mean the set in which we can make a selection from.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We have 3 slots to fill. This means r = 3.<BR>\n" );
document.write( "Order does NOT matter. Why not? <BR>\n" );
document.write( "Because all that matters is the grouping overall. <BR>\n" );
document.write( "A group like {A,B,C} is the same as {C,B,A}<BR>\n" );
document.write( "The only thing important really is the condition of the monitor (whether it's defective or non-defective).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the combination formula to get\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "24 C 3 = (24!)/(3!*(24-3)!)<BR>\n" );
document.write( "24 C 3 = (24!)/(3!*21!)<BR>\n" );
document.write( "24 C 3 = (24*23*22*21!)/(3!*21!)<BR>\n" );
document.write( "24 C 3 = (24*23*22)/(3!)<BR>\n" );
document.write( "24 C 3 = (24*23*22)/(3*2*1)<BR>\n" );
document.write( "24 C 3 = (12144)/(6)<BR>\n" );
document.write( "24 C 3 = <font color=red>2024</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is the answer to part A. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An alternative is to think of having 24 choices for slot A<BR>\n" );
document.write( "23 choices for slot B, and 22 choices for slot C\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "That makes 24*23*22 = 12144 different permutations. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Because order does NOT matter, we divide by 3! = 3*2*1 = 6 because there are 6 ways to order any single group of three.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Doing so yields: 12144/6 = <font color=red>2024</font><BR>\n" );
document.write( "leading to the same answer.<BR>\n" );
document.write( "This alternative method of thinking is shown in steps 5 & 6 of the combination formula method above.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "--------------------------------------------------------\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Part B)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The pool of possible choices goes from 24 to 19 since we're only considering the non-defective monitors now.<BR>\n" );
document.write( "So n = 19 for part B.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We still have 3 slots to fill. So r = 3.<BR>\n" );
document.write( "Like before, order isn't important. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use the combination formula.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "n C r = (n!)/(r!(n-r)!)<BR>\n" );
document.write( "19 C 3 = (19!)/(3!*(19-3)!)<BR>\n" );
document.write( "19 C 3 = (19!)/(3!*16!)<BR>\n" );
document.write( "19 C 3 = (19*18*17*16!)/(3!*16!)<BR>\n" );
document.write( "19 C 3 = (19*18*17)/(3!)<BR>\n" );
document.write( "19 C 3 = (19*18*17)/(3*2*1)<BR>\n" );
document.write( "19 C 3 = (5814)/(6)<BR>\n" );
document.write( "19 C 3 = <font color=red>969</font>\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which is the answer to part B\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Side Note:<BR>\n" );
document.write( "Subtract the results from part A) and part B) to get<BR>\n" );
document.write( "2024-969 = 1055<BR>\n" );
document.write( "This value of 1055 is the number of ways to select a trio of monitors where at least one is defective.<BR>\n" );
document.write( "\"At least one\" means \"one or more\".<BR>\n" );
document.write( "This bit of info is optional but may come in handy down the line.\r<BR>\n" );
document.write( "\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );