question

You don’t want a statistical distribution, you want a fixed ratio. In such scenario I recommend to setup an array of values which represent a ratio.

A really simple ratio would be

Array myratio = [1,2,3,4]; // four types equal distributed 

this array I assign to label. It is my default setup

Then I create items and choose randomly from this array an element by a discrete uniform distribution.

Array curRatio = myratio.clone(); 

This is my working array assigned to another label

int element = duniform(1,curRatio.length);
int nextType = curRatio[element];
curRatio.splice(element,1); // remove chosen element

if the working label array is empty of values, I fill it again from the default array.

An ratio of 2:1:1:1 would result in an Array of [1,1,2,3,4]. I think you get it now.

Your example is

4 times value 1; 5 times value 2; 7 times value 3; and so on.

Hint: my example is not a complete solution. It demonstrate how you achieve your aim. But the fun is, how you get it working yourself.