[SOLVED] counting problem - programs for radio station
Can someone tell me if my solution is correct? There is a different answer in the book.
Beethoven wrote 9 symphonies, and Mozart 27 piano concerts.
A station manager decides that on each successive night (7 days per week), a Beethoven symphony will be played, followed by a Mozart piano concerto, followed by a Schubert string quartet (of which there are 15). For roughly how many years could this policy be continued before exactly the same program would have to be repeated?
B=9, M=27, Q=27
Using the Multiplication Priniciple
BxMxQ = 9x27x15 = 3645 3-day sequences,
i.e. 3645 sets consisting of 3 days each.
3645 sets x 3 days each set = 10935 days
10935 / 365 days in a year = 29.95 years or approximately 30 years of non-repeating 3 day sequences.