You can answer this a couple of ways. You could calculate the permutation, or run a bunch of simulations.
A quick check for R packages that support this kind of thing (and I should say that I personally haven't worked with these yet), it looks like the Rdice package describes itself as "A collection of functions to simulate dice rolls and the like. In particular, experiments and exercises can be performed looking at combinations and permutations of values in dice rolls and coin flips, together with the corresponding frequencies of occurrences...", which seems like exactly what you're looking for on the simulation side of things.
A good way to move forward here would be to check out those packages that support these kinds of questions as a starting point. If you have questions or issues with your approach, pose it back here with a reproducible example.