Answer: 1000 different flags
Explanation:
So for the flag there are 10 color options and you need to have 3 different stripes. Where you are able to use a color more than once.
For the first stripe there are 10 options so it can be any of the 10 choices.
For the second option you are able to use any of the 10 colors again so it can be any of the 10 colors.
For the last option for stripe 3 you can pick from ay of the 10 colors so there are 10 color options is could be.
Now that you know the how many choices of color there can be for each stripe you multiple the color choice for each stripe by each other to get the number of combinations for different flags.
colors for stripe 1x colors for stripe 2x colors for stripe 3= # of different flags
10x10x10=1000
so there can be 1000 different 3 stripe flags that can be made with 10 colors