"Die"

If the number of different outcomes when 3 identical dice are thrown is $\text{x}$ then find the number of ways in which $\text{ x}$ 1's and $\text{ x}$ 2's can be arranged in a row so that at any point no. of 1's is greater than or equal to no. of 2's

If your answer is of the form $\frac{\binom{112}{56}}{s}$ find s. Write your answer as $\frac{s}{114}$