Question 1073337
Take one of the students that have repertoires of five numbers.
There are {{{5}}} different choices for the number that student will play.
For each of those choices, there will be many programs depending on the choices made for the other students.
Consider the other student with a repertoire of five numbers.
There are {{{red(5)}}} different choices for the number that student will play.
With those two students, each playing one piece,
you could make {{{5*red(5)=25}}} different programs.
The choices multiply.
There are {{{4}}} choices for each of the other four students.
Multiplying the number of possible choices for all the students,
you have
{{{5*5*4*4*4*4=25*4*4*4*4=100*4*4*4=100*64=6400}}} .