When given a problem in which you have to choose subsets of length k from a set with n elements and:
1.- The order does not matter, you can use the number of combinations formula:
[tex]C(n,r)=\frac{n!}{r!(n-r)!}.[/tex]2.- The order matters, you can use the number of permutations formula:
[tex]P(n,r)=\frac{n!}{(n-r)!}.[/tex]Therefore, using the first formula for part (b), and the second one for part (a) you get:
[tex]\begin{gathered} C(3,2)=\frac{3!}{2!(3-2)!}=3, \\ P(3,2)=\frac{3!}{(3-2)!}=6. \end{gathered}[/tex]