Answer: We are given five colors, Red Blue Green Purple and Yellow, We need to place them into two, and would like to know the total combinations, A The order matters, B Order does not Matter.
A-The order matters:
[tex]\begin{gathered} \text{slots =2 } \\ \text{Colors = =5} \end{gathered}[/tex]Therefore we have:
[tex]5\cdot4\cdot3\cdot2\cdot1=60\cdot2\cdot1=120\text{ ways}\rightarrow\text{ Because order mattered}[/tex]B-The order does not matter:
[tex]\frac{5!}{2!}=\frac{5\cdot4\cdot3\cdot2\cdot1}{2\cdot1}=60\rightarrow Because\text{ the order does not matter}[/tex]Note!, When the order does matter, we are counting each possibility twice, and when it does not, we only count once.
