My First Problem is Back!

There are 4 buttons in front of you, each with a different color, right beside it is a scoreboard showing your score. Starting from 0 points, your goal is to achieve exactly 386 points (because why not?), by pushing the buttons a total of 20 times.

If you push the red button, your score will increase by 17 points.
If you push the blue button, your score will increase by 41 points.
If you push the yellow button, your score will increase by 25 points.
If you push the green button, your score will increase by 11 points.

There are many ways to do this, 2 of them are listed below:
3 red, 4 blue, 2 yellow, 11 green
13 red, 2 blue, 2 yellow, 3 green

What is the total number of ways can this be done?

(Note: You do not have to push all 4 of the buttons at least once.)


This is one part of 1+1 is not = to 3.

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