document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172902>Question 1172902</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a class of 50 students 24 like football 21 basketball and cricket six like football and basketball 3 like basketball only, five like all three games, and 14 did not like any of the three games.\r<BR>\n" );
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document.write( "1.illustrate this information of Venn diagram <BR>\n" );
document.write( "2. Find the number of students who like<BR>\n" );
document.write( "      A. Football and cricket <BR>\n" );
document.write( "      B. Exactly one of the game <BR>\n" );
document.write( "      C. Exactly two of the game. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850799 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850799\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Absolutely, let's solve this problem step-by-step using a Venn diagram.\r<BR>\n" );
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document.write( "**1. Venn Diagram**\r<BR>\n" );
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document.write( "Let's use the following notation:\r<BR>\n" );
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document.write( "* F = Football<BR>\n" );
document.write( "* B = Basketball<BR>\n" );
document.write( "* C = Cricket\r<BR>\n" );
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document.write( "We are given:\r<BR>\n" );
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document.write( "* Total students = 50<BR>\n" );
document.write( "* n(F) = 24<BR>\n" );
document.write( "* n(B) = 21<BR>\n" );
document.write( "* n(F ∩ B) = 6<BR>\n" );
document.write( "* Students who like basketball  DISABLED_event_only=  3<BR>\n" );
document.write( "* n(F ∩ B ∩ C) = 5<BR>\n" );
document.write( "* Students who like none of the games = 14\r<BR>\n" );
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document.write( "Here's how we'll build the Venn diagram:\r<BR>\n" );
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document.write( "1.  **Start with the intersection of all three:**<BR>\n" );
document.write( "    * n(F ∩ B ∩ C) = 5. Place 5 in the center of the Venn diagram where all three circles overlap.\r<BR>\n" );
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document.write( "2.  **Football and Basketball:**<BR>\n" );
document.write( "    * n(F ∩ B) = 6. We know 5 like all three, so 6 - 5 = 1 student likes only football and basketball. Place 1 in the F ∩ B region.\r<BR>\n" );
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document.write( "3.  **Basketball Only:**<BR>\n" );
document.write( "    * 3 students like only basketball, place a 3 in the B only section of the venn diagram.\r<BR>\n" );
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document.write( "4.  **Basketball circle:**<BR>\n" );
document.write( "    * We know n(B)=21. We have 5+1+3=9 of those students accounted for. 21-9=12. We do not yet know how many of those 12 like cricket, so we will fill in the values that we can.\r<BR>\n" );
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document.write( "5.  **Students who like none:**<BR>\n" );
document.write( "    * 14 students like none of the games. Place 14 outside the circles.\r<BR>\n" );
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document.write( "6.  **Total within the circles:**<BR>\n" );
document.write( "    * 50 total students - 14 who like none = 36 students who like at least one sport.\r<BR>\n" );
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document.write( "7.  **Football circle:**<BR>\n" );
document.write( "    * n(F) = 24. We know 5+1=6 of those. 24-6=18. 18 students like football and cricket, or football only. We cannot yet determine the individual values.\r<BR>\n" );
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document.write( "8.  **Cricket values:**<BR>\n" );
document.write( "    * We can find the total amount of students that like cricket. 36 students total like at least one sport. 36 - 3 - 1 - 5 - 18 = 9. 9 students like cricket only or cricket and football. We cannot yet determine the individual values.\r<BR>\n" );
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document.write( "9.  **Completing the diagram:**<BR>\n" );
document.write( "    * We know that the remaining students that like basketball must total 12. Let x= the students that like basketball and cricket only. 12 = x+5. x=7. 7 students like Basketball and Cricket only.<BR>\n" );
document.write( "    * We know the students that like cricket total 9+7+5 = 21.<BR>\n" );
document.write( "    * We know that the football only students equal 24-1-5-students that like football and cricket only. 24-6-cricket and football  DISABLED_event_only=  football only. 21-5-7=9. 9 students like cricket only. 24-1-5 = 18. 21-9-5-7=0. 18-0=18. 18 students like football only.<BR>\n" );
document.write( "    * The Venn diagram is complete.\r<BR>\n" );
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document.write( "**2. Answers**\r<BR>\n" );
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document.write( "**A. Football and Cricket:**\r<BR>\n" );
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document.write( "* To find the number of students who like football and cricket, we add the students who like only football and cricket (0) and those who like all three (5): 0+5=5.<BR>\n" );
document.write( "* 5 students like football and cricket.\r<BR>\n" );
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document.write( "**B. Exactly One Game:**\r<BR>\n" );
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document.write( "* Add the number of students who like only football (18), only basketball (3), and only cricket (9): 18 + 3 + 9 = 30.<BR>\n" );
document.write( "* 30 students like exactly one game.\r<BR>\n" );
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document.write( "**C. Exactly Two Games:**\r<BR>\n" );
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document.write( "* Add the number of students who like football and basketball only (1), basketball and cricket only (7), and football and cricket only (0): 1 + 7 + 0 = 8.<BR>\n" );
document.write( "* 8 students like exactly two games.<BR>\n" );
document.write( " </SPAN>\n" );
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