a Pay attention to the wording. It says first a Beethoven Symphony will be played and then a Mozart Concerto.
B
b In addition to the number of ways we have from Part A, we have an additional factor of 15 when adding the Schubert string quartet to the program.
A
a 243
B
b 9.98 years
Practice makes perfect
a Pay attention to the wording. The radio station wants to play two pieces: a Beethoven symphony and then a Mozart concerto. This means we start with a Beethoven symphony and follow with a Mozart concerto. There are 9 Beethoven symphonies to choose from, which means we have 9 different songs to choose from.
From each of these branches, we have 27 Mozart concerto to choose from. Therefore, to obtain the total number of ways this can be done, we have to multiply 9 and 27.
9(27)=243
b From Part A, we know that there are 243 ways of playing a Beethoven symphony followed by a Mozart concerto. If we add a Schubert string quartet after that — and there are 15 of them — we have a total of 243(15)=3645 ways that the songs can be played. Since there are 365 days in a year, it would take 3645365≈ 9.98 years before the same program was repeated.
