The composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo piano). a. How many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto? b. 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?

Answer: Step 1 of 1 Given, the composer Beethoven wrote 9 symphonies, 5 piano concertos (music for piano and orchestra), and 32 piano sonatas (music for solo piano). a. We need to determine how many ways are there to play first a Beethoven symphony and then a Beethoven piano concerto. = 9P1 5P =1× 5 = 45. Hence, there are 45 ways to play first a Beethoven symphony and then a Beethoven piano concerto. b. 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. We need to check for how many years could this policy be continued before exactly the same program would have to be repeated. 9P1 5P ×12P = 15×32 = 1440 Using the Fundamental Counting Principle 1440 =3.945 4 years 365 days in a year Therefore, this policy be continued for 4 years before exactly the same program would have to be repeated.