Dice Roll Game Probabilities

Hello everyone, I have a bit of a probability question for you as it has been quite awhile since I have been in school, and I can’t remember the equations for figuring out probabilities.
I am developing a dice rolling game where-in players roll 1 to 3 6-sided dice of a particular color vs. another player. On one end, you have an attacker and on the other a defender. There are 5 different types of dice; Red, Orange, Yellow, Green, and Blue. When rolling, an attacking player will have so many ‘hits’ negated by the opposing player’s ‘blocks’. Each dice has a set amount of ‘hit’ sides and ‘block’ sides as listed below:
Red Dice= 5 Hit Sides, 1 Block Side (or think of it like 2-6 are hits, 1 is a block)
Orange Dice= 4 Hit Sides, 2 Block Sides (or think of it like 3-6 are hits, 1-2 is a block)
Yellow= 3 Hit Sides, 3 Block Sides (or think of it like 4-6 are hits, 1-3 is a block)
Green= 2 Hit Sides, 4 Block Sides (or think of it like 5-6 are hits, 1-4 is a block)
Blue= 1 Hit Side, 5 Block Sides (or think of it like 6 is a hit, 1-5 is a block)
As should be apparent, certain dice are better on offense and certain dice are better on defense. As an example, An attacking player rolls 3 Red dice, a defender counters with 3 Blue dice. The attacker rolls 3 hits, the defender rolls 2 blocks. The 2 blocks rolled by the defender negate 2 of the attackers hits; so when the final it tallied, the defender takes 1 hit.
A second example, The attacker then throws 2 Orange dice, and rolls 1 hit. The defender rolls 3 green and gets 2 blocks, negating the attackers hit. The defender gets 0 hits on him/her.
The problem I am having is figuring out the probability of certain rolls vs other rolls. Is there a formula that I could use to determine the probability of getting 1 hit, 2 hits, and 3 hits respectively for each type of dice vs the other dice?
I hope I am being descriptive enough. Below is a link to an Excel spreadsheet that is showing what I am trying to accomplish. I think this may clear it up better.
https://dl.dropboxusercontent.com/u/86705767/Probablilities.xlsx
If anyone can help, it would be very, very much appreciated! Thank you for your time and have a great day!