A symphony orchestra has in its repertoire 30 Haydn symphonies, 15 modern works, and 9 Beethoven symphonies. Its program always consists of a Haydn symphony followed by a modern work, and then a Beethoven symphony.
haydn <- 30
modern <- 15
beethoven <- 9
total <- haydn + modern + beethoven
options(scipen=999) #avoid printing in scientific notation...Answer: They can play 4050 different programs.
Answer: The order in which they play pieces from different composers doesn’t impact the number of combinations. The answer remains 4050. This problem is a bit to large to demonstrate this visually, but p.76 (fig 3.1) pf the text has good tree-visualization of the concept. Changing the order of the layers doesn’t change the number of potential paths.
Answer: Here we have an \(nCr\) problem. Under these constraints, there are 24804 possible programs.