Question

a classical music concert is to constist of 3 cello pieces, 3 choral works, and 3 pieces for piano. In how many ways can the program be arranged if a piano piece must come first

Answer 1

120,960 ways

Explanation:

Assuming that each piece is unique, then the order of each piece matters.

There are 9 pieces in total, there are 3 options for the first piece (3 piano pieces), and the remaining 8 pieces can be permuted. The number of possible arrangements is:

`n=3*(8!)/((8-8)!)\\ n=3*8*7*6*5*4*3*2*1\\n=120,960\ ways`

The program can be arranged in 120,960 ways.