Question

You are making a color pattern to go on your wall in your room. There are 3 spots in the pattern, for the first spot

you can choose red, blue, or purple. For the second spot you can choose green or yellow, and for the third spot you
can choose orange, grey, black, or gold. How many different color combinations are possible?

Answer 1

Given the following information

`\begin{gathered} \text{Spot 1=}\mleft\lbrace red,blue,purple\mright\rbrace \\ \text{Spot 2=}\mleft\lbrace green,yellow\mright\rbrace \\ \text{Spot 3=}\mleft\lbrace orange,\text{grey,black,gold}\mright\rbrace \end{gathered}`

The number of possible colors in spot 1 is 3

The number of possible colors in spot 2 is 2

The number of possible colors in spot 3 is 4

Thus the number of combinations taking one color at a time is given below

`\begin{gathered} Spot1\Rightarrow^3C_1 \\ \text{Spot 2}\Rightarrow^2C_1 \\ \text{Spot 3}\Rightarrow^4C_1 \\ \text{The number of combinations of three colors in the spots taking one color at a time is} \\ ^3C_1*^2C_1*^4C_1 \end{gathered}`
`\begin{gathered} ^3C_1*^2C_1*^4C_1=3*2*4 \\ ^3C_1*^2C_1*^4C_1=24\text{ ways} \end{gathered}`

Hence, the number of different color combinations that are possible is 24