Can you check this problem?
Jean has 5 different colors of markers: red, blue, green, orange, and purple. Two colors are used to make a sign. How many different combinations are possible? List them.
Ans: 10 possible combinations
red/blue, red/green, red/orange, red/purple, blue/green, blue/orange, blue/purple, green/orange, green/purple, and purple/orange
Correct, there are 10 of them and you found them all
there are ten of them
15
You are correct 10
To check the number of possible combinations, we need to use the concept of permutation. In this problem, we have 5 options for the first color and 4 options for the second color (since we cannot repeat colors).
To find the total number of combinations, we multiply the number of options for each color. So, 5 options for the first color multiplied by 4 options for the second color gives us:
5 x 4 = 20
However, we need to divide by 2 because the order of the colors does not matter. For example, red/blue is the same combination as blue/red.
So, the final number of combinations is:
20 / 2 = 10
These are the 10 possible combinations:
- red/blue
- red/green
- red/orange
- red/purple
- blue/green
- blue/orange
- blue/purple
- green/orange
- green/purple
- purple/orange