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Probability is the measure of the likelihood that an event will occur. When dealing with finite sets of possible outcomes, such as dice rolls, the probability of any specific outcome is calculated by dividing the number of ways this particular outcome can occur by the total number of all possible outcomes.

In the context of dice, if you're looking to find the probability of rolling a specific number on one die, the chances are 1 in 6 since there are six faces on a die and only one face with the number you desire. When multiple dice are involved, the calculations can become more complex, and understanding the underlying principles of combinatorics becomes essential.

Combinatorics is a branch of mathematics dealing with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is related to several other areas of mathematics, such as algebra, probability, and geometry, and is widely applied in fields such as computer science and statistics.

The fundamental rule of combinatorics, often called the counting principle, is the guiding force in determining the number of possible outcomes in a situation like multiple dice rolls. The counting principle explains that if you have two independent events, and one can happen in 'm' ways, while the other can happen in 'n' ways, then together they can happen in a total of \(m \times n \) ways. This principle can be extended to any number of events happening in sequence.

When it comes to dice outcomes, we're often interested in understanding all the possible results of rolling one or more dice. Each die is a cube with six faces, each showing a different number of dots, or pips, from 1 to 6. When a single die is rolled, there are 6 possible outcomes.

However, when multiple dice are rolled, such as in our original exercise involving 5 dice, we must use the counting principle to work out all potential outcomes. For each die rolled, there are 6 possible outcomes, and since the dice are distinct and the outcome of one doesn't affect the others, we multiply the number of outcomes for each die together, which gives us \(6^5 \) or 7776 possible combinations for five dice tossed simultaneously.

It's crucial to understand that these outcomes are all equally likely if the dice are fair, and this forms the basis of many probability calculations in games involving dice.