A dance group has 12 people from which 5 people need to be chosen to attend a national competition. Bob and Nancy are required to participate in the competition. Given this requirement, how many different five-member teams are possible?

Question

A dance group has 12 people from which 5 people need to be chosen to attend a national competition. Bob and Nancy  are required to participate in the competition. Given this requirement, how many different five-member teams are possible?

anonymous · Answer

@DisplayError  would you like to help me on this one also?

displayerror · Answer

Again, I'm rusty with probability, but I think combinations would be used again. 
For Bob:
From 2 (Bob or Nancy), choose 1 AND from the remaining 10 people, choose 4, so
C(2,1) * C(10,4)
I apologize if this is wrong, it's been a while since I've done probability

anonymous · Answer

@DisplayError sorry, I edited my question as there was an error!

displayerror · Answer

Would it just be C(10,3)? Only three spots are free, and there are 10 people available to fill those spots.

anonymous · Answer

ohhh you are right! but why is it only 10C3? I thought that I had to add the 12C2?