There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k?  Options
A) 8
B) 9
C) 10
D) 11
E) 12
There are k-2 members in the band, and k-4 members without Jim and Ellen.   (k-4)C2 = 6   (k-4)(k-5)/2 = 6   (k-4)(k-5) = 12 = 4*3   k = 8   The answer is 8.
<result>A</result>
There are k-2 members in a certain band, including Jim and Ellen. Two members are to be selected to attend the Grammy awards ceremony. If there are 6 possible combinations in which Jim and Ellen are not selected, what is the value of k?