in a class of 50 students, 20 play baseball, 15 play cricket and 11 play football. 7 play both baseball and cricket, 4 play cricket and football and 5 play baseball and football. if 18 students do not play any of these given sports, how many students play exactly two of these sports?	Choose the correct option.
A) 10  B) 46  C) 67  D) 68  E) 446
<gadget id="calculator">20 + 15</gadget>
<output>35</output>

<gadget id="calculator">35 + 11</gadget>
<output>46</output>

<gadget id="calculator">7 + 4</gadget>
<output>11</output>

<gadget id="calculator">11 + 5</gadget>
<output>16</output>

<gadget id="calculator">46 - 16</gadget>
<output>30</output>

<gadget id="calculator">30 + 18</gadget>
<output>48</output>

<gadget id="calculator">50 - 48</gadget>
<output>2</output>

<gadget id="calculator">5 - 2</gadget>
<output>3</output>

<gadget id="calculator">7 - 2</gadget>
<output>5</output>

<gadget id="calculator">4 - 2</gadget>
<output>2</output>

<gadget id="calculator">5 + 2</gadget>
<output>7</output>

<gadget id="calculator">3 + 7</gadget>
<output>10</output>

<result>A</result>
in a class of 50 students, 20 play baseball, 15 play cricket and 11 play football. 7 play both baseball and cricket, 4 play cricket and football and 5 play baseball and football. if 18 students do not play any of these given sports, how many students play exactly two of these sports?
add(subtract(5, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), add(subtract(7, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18))), subtract(4, subtract(50, add(subtract(add(add(20, 15), 11), add(add(7, 4), 5)), 18)))))
notice that 7 play both baseball and cricket does not mean that out of those 7 , some does not play football too . the same for cricket / football and baseball / football . [ color = # ffff 00 ] { total } = { baseball } + { 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 - - > { all three } = 2 ; those who play only baseball and cricket are 7 - 2 = 5 ; those who play only cricket and football are 4 - 2 = 2 ; those who play only baseball and football are 5 - 2 = 3 ; hence , 5 + 2 + 3 = 10 students play exactly two of these sports . answer : a .