Calculation of the possibilities having three processes with 3, 3 and 2 steps being interleaved.

gistfile1.java

import groovy.util.PermutationGenerator;

import java.util.LinkedList;
import java.util.List;

import com.google.common.collect.Ordering;

public class Choice {

	public static void main(String[] args) {
		List<Integer> values = new LinkedList<>();
		for (int i = 1; i <= 8; i++) {
			values.add(i);
		}
		PermutationGenerator<Integer> gen = new PermutationGenerator<>(values);

		int sum = 0;
		System.out.println("Total " + gen.getTotal());
		while (gen.hasNext()) {
			if (isValid(gen.next())) {
				sum++;
			}
		}
		System.out.println(sum);
	}

	private static boolean isValid(List<Integer> list) {
		List<Integer> p1 = new LinkedList<>();
		List<Integer> p2 = new LinkedList<>();
		List<Integer> p3 = new LinkedList<>();

		for (Integer i : list) {
			if (i < 4) {
				p1.add(i);
			} else if (i < 6) {
				p2.add(i);
			} else {
				p3.add(i);
			}
		}

		Ordering<Integer> ordering = Ordering.natural();

		return ordering.isOrdered(p1) && ordering.isOrdered(p2) && ordering.isOrdered(p3);
	}
}