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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?

Answer :

pedrocarratore

Answer:

3.945 years

Step-by-step explanation:

To answer this problem, one must know that Beethoven has composed 32 piano sonatas, 9 symphonies and 5 piano concertos.

The number of different arrangements that can be made by playing a sonata, then a symphony and then a piano concerto is:

[tex]n=32*9*5=1,440[/tex]

If a year has 365 days, the number of years that this daily policy could be continued before exactly the same program would have to be repeated is:

[tex]y=\frac{1,440}{365}=3.945\ years[/tex]

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