There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 66 possible combinations in which Michael is not selected, what is the value of n?  Pick one:  A) 11  B) 12  C) 13  D) 14  E) 15
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) = 132 = 12*11   Thus, n = m + 1(Michael) = 13   The answer is 13.
<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 66 possible combinations in which Michael is not selected, what is the value of n?