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.)

Answer:3 years, 11 months and 10 daysStep-by-step explanation:Beethoven wrote 32 piano sonatas 9 symphonies 5 piano concertos By the fundamental principle of counting there are 32 times 9 times 5 ways of combining these pieces in the required order. 32 times 9 times 5 = 1,440 As there are 365 days in a year, the policy decided by the manager could be continued during 1,440/365 = 3.9452 years. But 3.9452 years = 3 years + 0.9452 years. As 1 year equals 12 months 0.9452 years = 11.3424 months 11.3424 months = 11 months+0.3424 months As 1 month = 30 days 0.3424 months = 10.27 days = 10 days rounded to the nearest integer So, the manager could continue this policy for 3 years, 11 months and 10 days without repeating the program.