# Probability and Statistics for Engineering and the Sciences (9th Edition) Edit editionThis problem has been solved:Solutions for Chapter 2Problem 31E: 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?

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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?

From the given information,

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

(a)

There are **9** possibilities to start with **symphonies** and after the symphony there are 5 choices of choosing piano concertos.

Therefore, total number of choices to play symphony followed by a piano concerto is calculated as follows:

Therefore, there are 45 ways to play first symphony and then a piano concerto.

## Corresponding textbook

**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?

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