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 15 possible combinations in which Jim and Ellen are not selected, what is the value of k? Choose the correct 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)102 = 15   (k-4)(k-5)/2 = 15   (k-4)(k-5) = 30 = 6*5   k = 10   The answer is 10.
<result>C</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 15 possible combinations in which Jim and Ellen are not selected, what is the value of k?