In a class of 50 students, 20 play Rugby, 15 play Cricket and 11 play Football. 7 play both Rugby and Cricket, 4 play Cricket and Football and 5 play Rugby and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?  Choices: A) 46 B) 667 C) 45 D) 24 E) 10
Notice that7 play both Rugby and Cricket does not mean that out of those 7, some does not play Football too. The same for Cricket/Football and Rugby/Football.   [color=#ffff00]{Total}={Rugby}+{Cricket}+{Football}-{HC+CH+HF}+{All three}+{Neither}For more checkADVANCED OVERLAPPING SETS PROBLEMS   [/color]   50=20+15+11-(7+4+5)+{All three}+18 --&gt; {All three}=2;   Those who play ONLY Rugby and Cricket are  7-2= 
<gadget id="calculator"> 7-2</gadget>
<output>5</output>
5;   Those who play ONLY Cricket and Football are  4-2= 
<gadget id="calculator"> 4-2</gadget>
<output>2</output>
2;   Those who play ONLY Rugby and Football are   5-2= 
<gadget id="calculator">  5-2</gadget>
<output>3</output>
3;   Hence, 5+2+3=10 students play exactly two of these sports.   Answer: 10.
<result>E</result>
In a class of 50 students, 20 play Rugby, 15 play Cricket and 11 play Football. 7 play both Rugby and Cricket, 4 play Cricket and Football and 5 play Rugby and football. If 18 students do not play any of these given sports, how many students play exactly two of these sports?