Issue: Probability formula for pattern sets

Hello,

As a side project a friend and I are trying create a game that involves 4 sided dice where for certain situations will call for certain pattern sets as opposed to the dice adding to a set number. The Number value of the individual die are not important. For the purpose of example we will use ABCD.

In our current desire of this pattern system, different factors are incorporated that lead to a Dice Roll, of which, is composed of different parts. The number of required total dice, for this example 5, and the pattern sets needed.

'A', we want, to be a botch value, unusable. B: the static value, C and D: variable values.

If the situation calls for 3 static and 2 variable. What would be the probability if I am using, say 6 dice.

I am basically looking for a way to find a formula that will cover all the factors and supply me with some perspective of the difficulty of any particular roll. Something that can also work for different amount dice used and needed, and incorporate the effects of changing the amount of static/variable dice needed to successfully complete the roll.

My friend and I are proudly adept at comprehending mathematics, however, we are not mathematicians and lack proper understanding of complex statistics and probabilities. It was would be very much appreciated if some light could be shed to fill us in on whether our idea is usable or just to complicated and needs to be rethought.

Thank you.

p.s. My apologies if I haven't properly conveyed the idea and have only concocted a confusing clusters of words. haha(Happy)