Statistics questions

Question

If I have 30 people and a group of six, I want 1 player to be a constant how many groups can I have with that one player being the constant.?

Answer 1

If you were to choose a group of six from 30 people with no constraints you could do it in ₃₀C₆ ways, where  

 

₃₀C₆ = 30!/(6!*(30-6)!)  

 

If you are going to require that 1 player be in all the groups, then that means that you are going to choose the other 5 people in the group from the 29 remaining people, which can be done in ₂₉C₅ ways.