MathDB

Brandon wants to split his orchestra of

20

violins,

15

violas,

10

cellos, and

5

basses into three distinguishable groups, where all of the players of each instrument are indistinguishable. He wants each group to have at least one of each instrument and for each group to have more violins than violas, more violas than cellos, and more cellos than basses. How many ways are there for Brandon to split his orchestra following these conditions?

Problem Statement