My First Problem is back!

Number Theory Level pending

In front of you are 4 buttons, each with a different color, right beside it is a scoreboard showing your score.

If you push the red button, your score will increase by 17 points.

If you push the blue button, you will get 41 points.

If you push the yellow button, you will gain 25 points.

If you push the green button, you get 11 points.

And the rule is, you must push the buttons a total of 20 times.

Starting from 0 points, let's say your goal is to achieve exactly 386 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?


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