There are e 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 e?  Select
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, e = m + 1(Michael) = 12   option 12
<result>B</result>
There are e 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 e?