there might be different ways but i do it this way.

you create an array with the length of your exisiting shapes and fill it with numbers from 0-n
you then shuffle this array to change their order.
If you know pick lets say the first 10 shapes out of this array, they are randomly chooses but never the same.

hope it makes sense.
should look something like this :

1. Integer[] shapeArray;
   int setSize = 20;
   int numberOfShapes = 10;
   shapeArray = new Integer[setSize];
   
   for(int i = 0; i<setSize;i++){
       shapeArray[i] = i;
     }
   
     Collections.shuffle(Arrays.asList(shapeArray));
   
   }
   
   
   
   
   for(int i = 0; i<numberOfShapes;i++){
   
   shape(shapeArray[i]+".svg",x,y);
   
   }
   

i slightly edited the code.
try again, it should return, 10 random numbers out of the 20 without printing a number twice


Integer[] shapeArray;
int setSize = 20;
int numberOfShapes = 10;
shapeArray = new Integer[setSize];

for(int i = 0; i<setSize;i++){
  shapeArray[i] = i;
}

Collections.shuffle(Arrays.asList(shapeArray));

for(int i = 0; i<numberOfShapes;i++){
  println(shapeArray[i]);
}

1. // no need to shuffle, imo.
   
2. for (i = 0 ; i < (int)random(1, 3) ; i++)  {
3.   myDraw(shapes[(int)random(NUMBER_OF_SHAPES)]);
4. }

Collections is a Java class: Collections.
Arrays would have been better (not need to go through an ArrayList)... except there is no Arrays.shuffle! (strangely).

I'm still confused. I see how all this can work with simple data types such as integers but working with objects such as Strings makes it difficult. I can't seem to translate that information. 

hmm not sure where the problem is.
you can use these integers to choose from any datatype you want. an array of objects, or strings. etc.

This is as far as I got Cedric but as you can see I'm not coding this correctly :

i would recommend doing it like this, fill the Shape array at the beginning and then pick them on runtime

1. Integer[] shapeArray;
   int setSize = 9;
   int numberOfShapes;
   shapeArray = new Integer[setSize];
   PShape[] c = new PShape[setSize];
   for(int i = 0; i<setSize;i++){
   c[0] = loadShape("forme_" + nf(i, 3) + ".svg");
   }
    
    numberOfShapes = int(random(1,4));
    
   
   for(int i = 0; i<setSize;i++){
     shapeArray[i] = i;
   }
   
   Collections.shuffle(Arrays.asList(shapeArray));
    
   for(int i = 0; i<numberOfShapes;i++){
      shape(c[i], 25, 25);
   }
   

Thanks Cedric for the reply. I finally found the answer. You have to call shapeArray within shape, in that way we always have a random composite of either one, two or three shapes from the list of 19. Again, thanks for your time and efforts.