There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 45 possible combinations in which Michael is not selected, what is the value of n?  Options.
A) 11
B) 12
C) 15
D) 18
E) 22
The combinations of two people, in which Michael was not selected = 45   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) = 90 = 10*9   Thus, n = m + 1(Michael) = 11   The answer is 11.
<result>A</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 45 possible combinations in which Michael is not selected, what is the value of n?