In this module you will be introduced to the definitions, symbols and formulas for permutations and factorial notation. A variety of examples will illustrate the Fundamental Counting Principle and how it can be applied to problems for finding the number of permutations using all or only some of the objects. Permutations without repetition and permutations with repetitions will be analyzed with corresponding examples.

In this module you will be introduced to the definition, notations and formulas for combinations as well as understanding the relationship between permutations and combinations. A variety of examples will illustrate how these concepts can be applied to problems for finding the number of combinations or groups using all or only some of the objects.

In this module you will be introduced to probability theory – a branch of mathematics that furnishes a quantitative measure for uncertainty. You will also learn about sample spaces, possible outcomes, impossible events, certain events, and probability values. You will compare two ways of representing all possible outcomes: sample spaces and tree diagrams and also how Venn diagrams can be helpful in visualizing probability concepts.

In this module you will be introduced to the two types of probability theory: empirical or experimental probability that is based on actual experiments and theoretical probability that is based on the ratio of the number of favorable outcomes to the number of possible outcomes.

In this module you will further investigate the concepts of probability of impossible events, certainty, and those that are neither. You will also learn about probability sums, complementary events, and computing simple probabilities.

In this module you will learn how to distinguish between probabilities that involve mutually exclusive events, where there is nothing in common with the events, and those that are mutually inclusive, where the events share something in common. The formula for each probability will be stated in terms of symbolic logic notation and examples of each will be explained.

In this module you will be recalling the Fundamental Counting Principle and how it can be expanded to apply to the Fundamental Probability Principle. Formulas for each will be stated in terms of set notation.

In this module you will be analyzing the method used to compute the probability of independent events and the concept of “with replacement.” Attention will also focus on analyzing the method for computing the probability of dependent events with the qualification of “without replacement.”

In this module you will be introduced to Bernoulli experiments where only two possible outcomes are possible. You will learn about the conditions necessary to conduct these experiments. The formulas for computing the probability of getting exactly ‘x’ successes in ‘n’ trials and for computing the probability of getting at least ‘x’ successes in ‘n’ trials will be stated along with appropriate examples.

In this module you will apply the Binomial Theorem to expand any binomial to the nth power, where n is a natural number or to find a specific term in the expansion. The skeletal structure of these expansions will be described and Pascal’s Triangle, which is an array of the coefficients for a binomial expansion, will be explained. Numerous examples will be analyzed.

In this module you will learn how to find the probability of an event when we know that another event affecting the desired outcome has already occurred. The formulas for this probability and various examples will be explained.

In this module you will be given a comprehensive list of the definitions, notations, and formulas useful in finding combinations, permutations and various probabilities.