(a)

Scenario: The composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo piano).

Problem: How many ways are there to play first a Beethoven piano concerto and then a Beethoven symphony?

Process: The phrase "how many ways" indicates we are finding the number of combinations of the piano concertos and symphonies. There are 5 piano concertos which can be played. After a given piano concerto, there are 9 symphonies which can be played.

Answer: 45.

(b)

Problem: The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven symphony will be played followed by a Beethoven piano concerto followed by a Beethoven piano sonata. For how many years could this policy be continued before exactly the same program would have to be repeated? (Assume there are 365 days in a year. Round your answer up to the nearest whole number.)

Process: We need to find the number of combinations of symphonies, piano concertos, and piano sonatas using the same process as before. Since one combination will be played every day, and since there are 365 days in a year, we can find the number of years where a unique combination plays by dividing the total number of combinations by 365 and then rounding.

Answer: 4.