I am working through the following question:
If Larry, Moe and Curly visit a town with 7 churches, then (a) in how many ways can all three visit the same church, and (b) in how many ways will they not all choose the same church?
For a) I have the following calculation:
$$\binom{7}{1} = 7$$
Is it that simple or am I missing something?
For b) I have this:
$$P_3^7 = 210$$
Am I on the right path, or have I made any errors? Thanks for your help!