Roll four 6D. Ignore the largest result. Will the sum of the remaining results be less than 8?

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I thought I could make an overview of possible outcomes when rolling four dice. So look at possible sums when rolling four dice, 4-24, and which combinations that give these sums. Then one can exclude the largest number in each combination and see which ones give sum less than 8. This took a very long time to do manually and I therefore thought that one might be able to create a python program that produces such an overview. Is there anyone who can help me create such a code?