There are r members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of r? Choose the correct choice: A) 11 B) 12 C) 15 D) 18 E) 22
Combinations of two persons, in which Michael was not selected = 55   number of ways two persons can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael, then m*(m-1) = 110 =&gt; m=11   Thus, r = m + 1(Michael) = 12   option 12
<result>B</result>
There are r members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of r?