First time poster, long time lurker.

Java

package challenge.easy236;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;
import java.util.Random;

public class TetrisPieceGeneratorSmall{
    private static List<Character>    pieces            = Arrays.asList('O', 'I', 'S', 'Z', 'L', 'J', 'T');
    private static int                piecesWanted    = 50;

    public static void main(String[] args){
        String generatedPieces = generate();
        System.out.println("Generated Pieces: " + generatedPieces);
        System.out.println("Are Generated Pieces Valid? " + verify(generatedPieces));
    }

    private static String generate(){
        List<Character> bag = new ArrayList<Character>(pieces.size());
        String output = "";
        Random random = new Random();
        for (int piecesGenerated = 0; piecesGenerated < piecesWanted; piecesGenerated++){        //Keep on grabbing pieces until 50 pieces have been generated.
            if (!bag.isEmpty()) {        //Grab a piece from the bag if it still has a piece within.
                output += bag.remove(random.nextInt(bag.size()));        //Add a random removed piece from the bag to the output.
            }
            else{
                bag.addAll(pieces);        //Refill bag.
            }
        }
        return output;
    }

    private static boolean verify(String toVerify){
        List<String> bags = new ArrayList<String>();
        String currentBag = "";
        for (int i = 0; i < toVerify.length(); i++){        //For every character in the toVerify string.
            if (currentBag.length() < pieces.size()) {        //If the current bag is smaller then the default bag size.
                currentBag += toVerify.charAt(i);        //Add current piece in toVerify string to current bag.
            }
            else{        //Bag is complete.
                bags.add(currentBag);        //Add current bag to list of bags.
                currentBag = "" + toVerify.charAt(i);        //Set current bag to current character only.
            }
        }
        if (currentBag != "") {        //If there are any leftover pieces in current bag.
            bags.add(currentBag);        //Add last leftover pieces to bag list.
        }
        for (String bag : bags){        //For every bag collected.
            for (Character piece : bag.toCharArray()){        //For every piece within current bag (Piece1)
                for (int i = 0; i < bag.length(); i++){        //For every piece within current bag (Piece2)
                    if (bag.indexOf(piece) != i && piece.equals(bag.charAt(i))) {        //If the location of Piece1 is not the same as Piece2 and Piece1 is the same as Piece2
                        return false;
                    }
                }
            }
        }
        return true;        //The string has no bags with duplicate characters, so it's valid!
    }
}