for letters a,b,c,d,e,f

-how many arrangements can there be with 'a' and 'b' next to eachother?

(5! x 2)?

-how many arrangements can there be with 'a' and 'b' not next to eachother?

(6!) - (5! x 2)?

-how many arrangements can there be with 'a' and 'b' next to eachother, but with 'a' and 'c' not next to eachother?

thanks for the help.