Given n things in a certain order, the number of "derangements" or 
ways to rearrange them so that none of them are in the same position
they were in before rearranging is given by the formula !n, known as 
n-subfactorial.

The formula for !n is 



So the number of ways no trumpet player gets his or her own trumpet back is



[Incidentally, FYI, those 9 rearrangements of 

1,2,3,4 are

2,1,4,3
2,3,4,1
2,4,1,3
3,1,4,2
3,4,1,2
3,4,2,1
4,1,2,3
4,3,1,2
4,3,2,1]

The total number of arrangements is 4! = 24.

So the desired probability is 9 ways out of 24.

That's 9/24

Edwin