document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158215>Question 1158215</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following problems can be solved using the principle of inclusion-exclusion. Give the solutions by<BR>\n" );
document.write( "naming sets A1<BR>\n" );
document.write( ", A2<BR>\n" );
document.write( ", ... , Ak such that either the set or the complement of the set is counted by the<BR>\n" );
document.write( "inclusion-exclusion formula.<BR>\n" );
document.write( "(1) How many n-digit decimal sequences (using the digits 0 − 9) are there in which the digits 1, 2 and<BR>\n" );
document.write( "3 all appear?<BR>\n" );
document.write( "(2) How many ways are there of rolling a sided die 10 times in a sequence such that all 6 faces<BR>\n" );
document.write( "appear?<BR>\n" );
document.write( "(3) How many positive integers less than or equal to 420 are relatively prime to 420 ?<BR>\n" );
document.write( "(hint: 420 = 2 )<BR>\n" );
document.write( "2<BR>\n" );
document.write( "· 3 · 5 · 7<BR>\n" );
document.write( "(4) How many arrangements of 52 letters, 2 A’s, 2 B’s, 2 C’s, etc. with no pair of identical letters<BR>\n" );
document.write( "exist?<BR>\n" );
document.write( "(5) How many ways are there of dealing a 13 card hand with at least one void in a suit?<BR>\n" );
document.write( "(6) How many 13 card hands have at least one picture card (i.e., J, Q, K, A)? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781164 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781164\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "The &nbsp;RULE, &nbsp;the &nbsp;POLICY &nbsp;and the &nbsp;REQUIREMENT &nbsp;of this forum is\r<BR>\n" );
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document.write( "<H2>&nbsp;&nbsp;&nbsp;&nbsp;ONE and ONLY ONE problem per post.</H2>\r<BR>\n" );
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document.write( "And those who violate this rule, &nbsp;work &nbsp;<U>against</U> &nbsp;their own interests.\r<BR>\n" );
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document.write( "At this forum, &nbsp;I explained it just &nbsp;2937 &nbsp;times.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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