Answer:
a) 20 ways
b) 10ways
Explanations:
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]
