There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 78 possible combinations in which Michael is not selected, what is the value of n?	Choose one.
A) 12  B) 13  C) 14  D) 15  E) 16
The combinations of two people, in which Michael was not selected = 28   The number of ways two people can be selected from m people = m*(m-1)/2   Let m be the number of people excluding Michael.   Then m*(m-1) = 156 = 13*12   Thus, n = m + 1(Michael) = 14   The answer is 14.
<result>C</result>
There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 78 possible combinations in which Michael is not selected, what is the value of n?