Answers to Sections 3 and 4 of Marcel B. Finan's "A Probability Course for the Actuaries"

These answer keys are meant to assist students using Marcel B. Finan's A Probability Course for the Actuaries. With Dr. Finan's permission, Mr. Stolyarov wrote solutions for the problems in his study guide and is endeavoring to make the answer keys to each section publicly available. You can see his full List of Answer Keys here. Do the problems at the end of each section and then check your answers with these keys.

Dr. Finan's study guide is an excellent resource for those preparing to take Actuarial Exam 1/P on probability.

Problems that require numerical answers are answered here, but it is still the responsibility of the student to provide his or her own work for these problems. These answers are meant to enable students to independently verify the correctness of their reasoning by checking to see if the end result they obtained is correct. Questions from the study guide that require proofs or diagrams are not addressed here, as the end result of those questions is known in advance, and it is the responsibility of the student to provide the procedure for getting there.

Section 3.

Answer 3.1a. 100 ways

Answer 3.1b. 900 ways

Answer 3.1c. 5040 ways

Answer 3.1d. 90000 ways

Answer 3.2a. 336 finishing orders

Answer 3.2b. 6 finishing orders

Answer 3.3. 6 choices of outfits

Answer 3.4. 90 ways

Answer 3.6. 36 ways

Answer 3.7. 380 ways

Answer 3.8. 6,497,400 ways

Answer 3.9. 5040 ways

Answer 3.10. 3840 ways

Section 4.

Answer 4.1. m=9 and n=3

Answer 4.2a. 456,976 words

Answer 4.2b. 358,800 words

Answer 4.3a. 15,600,000 possible license plates

Answer 4.3b. 11,232,000 possible license plates

Answer 4.4a. 64,000 possible combinations

Answer 4.4b. 59,280 possible combinations

Answer 4.5a. 479,001,600 arrangements

Answer 4.5b. 604,800 arrangements

Answer 4.6a. 5

Answer 4.6b. 20

Answer 4.6c. 60

Answer 4.6d. 120

Answer 4.7. 20 ways

Answer 4.8a. 362,880 ways

Answer 4.8b. 15,600 ways

Answer 4.9. m=13; n=1 or n=12

Answer 4.10. 11,480 possible choices

Answer 4.11. 300 handshakes

Answer 4.12. 10 ways

Answer 4.13. 28 ways

Answer 4.14. 4060 ways

Answer 4.15. The number of permutations of a set of objects is usually greater.