Yes, you can create your own list to pick problems from by following the steps below:
Go to the 'Problems' link
Click on the “plus” sign next to “ALL”
A pop-up window will open up shown as below. Enter the name of your list to “Name” section.
After hitting “create” go back to “ALL” and select the problems you like to add to your list.
After selecting the problems you can add them to your list by clicking on the “More” button and selecting the list you like to add the problems to.
Then the problems will be added to your list, which you can use as you are creating assignments.
To remove a pre-existing list: first, select the list you would like to remove and then go to the "More" button to select the "Remove list". 