Discrete Mathematics for Computer Science: Counting and Probability

HKUST develops counting methods before using them to reason about probability. Permutations, combinations and binomial identities lead into inclusion-exclusion, conditional probabilities, Bayes’ rule and random variables. It suits learners who want to identify the structure of a finite problem and explain why a particular count or probability calculation applies.

What you will learn

• Distinguish permutations, combinations and counting rules.
• Apply inclusion-exclusion to overlapping cases.
• Reason about conditional probability and random variables.

Who this suits

Beginners building discrete-mathematics foundations for computer science, comfortable following elementary algebra and willing to check assumptions about equally likely outcomes.

Before you enroll

Work through examples with a written argument rather than relying on an answer alone. Check definitions, quantifiers and boundary cases, and distinguish a model’s assumptions from the situation it represents. These courses take different routes through discrete mathematics; compare their preparation requirements and topic coverage before choosing a starting point.

Coursera offers paid enrollment or subscription access. Check the enrollment screen for assessment and certificate terms, trials and any financial-aid options. Provider access terms can change; review them before paying.

Put it into practice

Create a finite selection problem with an overlap between cases. Count the outcomes two ways, then define a probability question and state the assumptions used in your calculation.

Source and review

This overview is based on the provider's published information, checked on 12 October 2026. It is an editorial assessment, not a claim that we completed the resource. Time filters are approximate study ranges; projects and exercises can take longer.

View the curriculum and current access options at Coursera.

How YellowCourse describes and checks learning resources.