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 28 possible combinations in which Jim and Ellen are not selected, what is the value of k? Choose the most appropriate option
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 = 28   (k-4)(k-5)/2 = 28   (k-4)(k-5) = 56 = 8*7   k = 12   The answer is 12.
<result>E</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 28 possible combinations in which Jim and Ellen are not selected, what is the value of k?