demo, Java - rextester

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//'main' method must be in a class 'Rextester'.
//Compiler version 1.8.0_111

import java.util.*;
import java.lang.*;

class Rextester
{  
    public static < T > T getRandomSetEntry(Set<T> set) {
        int size = set.size();
        int item = new Random().nextInt(size);
        int i = 0;
        for (T obj : set) {
            if (i == item)
                return obj;
            i++;
        }

return null;
    }

public static void main(String args[])
    {
        Map<String, Set<String>> namesForGroup = new HashMap<>();
        Set<String> set1 = new HashSet<>();
        set1.add("a");
        set1.add("b");
        set1.add("c");
        set1.add("d");
        Set<String> set2 = new HashSet<>();
        set2.add("e");
        set2.add("f");
        set2.add("g");
        set2.add("h");

namesForGroup.put("Grp1", set1);
        namesForGroup.put("Grp2", set2);

Set<Map.Entry<String, Set<String>>> set = namesForGroup.entrySet();
        Map.Entry<String, Set<String>> entry = getRandomSetEntry(set);
        String key = entry.getKey();
        String value = getRandomSetEntry(entry.getValue());
        System.out.println("key: " + key + ", value: " + value);
    }
}

[ + ] Show input
Compilation time: 0.62 sec, absolute running time: 0.14 sec, cpu time: 0.06 sec, memory peak: 18 Mb, absolute service time: 0,76 sec