a) 20 ways
b) 10ways
Permuation has to do with arrangement (order matters here) while combination has to do with selection (order of choice does not matter).
a) Suppose we want to choose 2 colors, without replacement, from the 5 colors red, blue, green, purple, and yellow, the number of ways this can be done if the order of the choices is relevant is given as;
[tex]\begin{gathered} 5P_2=\frac{5!}{(5-2)!} \\ 5P_2=\frac{5!}{3!} \\ 5P_2=\frac{5\times4\times3\times2!}{3\times2!} \\ 5P_2=5\times4 \\ 5P_2=20ways \end{gathered}[/tex]b) If the order of the choices is not relevant, this will be a case of selection (combination rule) as shown:
[tex]\begin{gathered} 5C_2=\frac{5!}{(5-2)!2!} \\ 5C_2=\frac{5!}{3!2!} \\ 5C_2=\frac{5\times4\times3!}{3!\times2!} \\ 5C_2=\frac{5\times4}{2} \\ 5C_2=10ways \end{gathered}[/tex]