By Yufeng Guo
The autumn 2013 variation of Guo's handbook for the 1st SOA/CAS actuarial examination P.
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Additional resources for Deeper Understanding, Faster Calculation—Exam P Insight and Shortcuts (Fall 2013 Edition)
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Permutations if each ball is distinct. However, we have identical balls and we need to remove the permutations by these identical balls. So r1 balls are identical and have r1 ! permutations; r2 balls are identical and have r2 ! permutations. … rk balls are identical and have rk ! permutations. Thus, we need to divide n ! rk ! to get the distinct number of permutations. rk )! n! rk ! rk ! Example. You are using six letters A, A, A, B, B, C to form a six-letter symbol. How many distinct symbols can you create?
Not very likely. It takes too much work for you to solve it. It takes too much work for SOA to write this question and come up with an answer too. However, if this kind of difficult problem does show up, you will probably want to skip it and focus on easier problems, unless your goal is to score a 10. How to tackle the problem in 3 minutes There are 2 approaches to “sort out who did what” – the formula-driven approach and the common sense approach. You might want to familiarize yourself with both approaches and choose one that you like better.
Deeper Understanding, Faster Calculation—Exam P Insight and Shortcuts (Fall 2013 Edition) by Yufeng Guo