A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 5 students hold membership in both organizations, how many different committee are possible? Pick one
A) 215  B) 275  C) 325  D) 385  E) 495
student government + the student advisory board consists of  9 + 8= 
<gadget id="calculator"> 9 + 8</gadget>
<output>17</output>
17 members.   5 students hold membership in both, so they were counted twice.   The total number of people to choose from is 17 - 5= 
<gadget id="calculator">17 - 5</gadget>
<output>12</output>
12   The number of ways to choose 8 members from 12 is 12C8= 495   The answer is 495.
<result>E</result>
A university needs to select an eight-member committee on extracurricular life, whose members must belong either to the student government or to the student advisory board. If the student government consists of 9 members, the student advisory board consists of 8 members, and 5 students hold membership in both organizations, how many different committee are possible?