Distinguishable Permutation Examples ​​(SOA Exam P – Probability – General Probability Module)

Master distinguishable permutations for SOA Exam P (Probability). We start with the Fundamental Counting Principle, then handle permutations when some items are identical, and show how these questions connect to combinations. Worked examples include the marble arrangement problem and multiple bookshelf problems. Clear step-by-step reasoning, common pitfalls, and exam tips throughout.

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After completing this video you should be able to:

Calculate probabilities using combinatorics, such as combinations and permutations.

Fundamental Counting Principle (FCP): If there are 𝑚 ways of performing Task 1 and 𝑛 ways of performing Task 2, then there are 𝑚∙𝑛 ways of performing the job consisting of Tasks 1 and 2. This is easily generalized to jobs with more than 2 tasks.

Example given in the video:

Example 1:
A bag contains 4 marbles; a red marble with a 1 painted on it, a red marble with a 2 painted on it, a green marble with a 1 painted on it, and a green marble with a 2 painted on it. Determine the number of ways to arrange the marbles in a row.

Example 2:
A library bookshelf contains 5 identical looking math books and 4 identical looking history books. Determine the number of distinguishable permutations of the 9 books on the shelf.

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