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 piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. 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.)

Question

Hamza Salas

Mathematics

23 August, 00:26

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 piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto. 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.)

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Answers (1)

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Orlando Kaufman · Answer 1

a. 45ways b. 3.95years

Step-by-step explanation:

The composer Beethoven wrote 9 symphonies, 5 piano concertos, and 32 piano sonatas

(a) There are 9*5 ways to play first a Beethoven symphony and then a Beethoven piano concerto

9*5=45

(b) The manager of a radio station decides that on each successive evening (7 days per week), a Beethoven piano sonata will be played followed by a Beethoven symphony followed by a Beethoven piano concerto.

there are 32*9*5 combinatios of piano sonata followed by a Beethoven symphony followed by a Beethoven piano concerto.

32*9*5=1440

1440 nights / 365 days = 3.95 years