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JNumberTools is the combinatorics and number-theory library which provides useful APIS related to said topics

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import io.github.deepeshpatel.jnumbertools.base.JNumberTools;

import java.util.List;
import java.util.stream.IntStream;

public class Scrap {
    public static void main(String[] args) {
//Every 10^18 th lexicographical combinations of -
// any 10 distinct small alphabets and
// any 12 distinct capital alphabets and
// any 3 symbols with repetition allowed and
// all subsets in size range [10,20] of a set of numbers in [0,20)

        var smallAlphabets = IntStream.rangeClosed('a', 'z').mapToObj(c -> (char) c).toList();
        var capitalAlphabets = IntStream.rangeClosed('A', 'Z').mapToObj(c -> (char) c).toList();
        var symbols = List.of('~','!','@','#','$','%','^','&','*','(',')');
        var numbers = IntStream.rangeClosed(0, 20).boxed().toList();

        JNumberTools.cartesianProduct()
                .complexProductOf(10, smallAlphabets) //distinct
                .andDistinct(12, capitalAlphabets) //distinct
                .andMultiSelect(3, symbols) // repetition allowed
                .andInRange(10, 20, numbers) // all subsets in size range
                .lexOrderMth(1000_000_000_000_000_000L, 0).stream().toList();

        //System.out.println(list.size());
        //System.out.println(list);

    }


}