How many three digit numbers can be composed of the numbers 1, 2, 3, 4 and 5 without repetition, and 2 and 3 are not adjacent?

How many three digit numbers can be composed of the numbers 1, 2, 3, 4 and 5 without repetition, and 2 and 3 are not adjacent?

A(5,3)-C(3,1)*A(2,2)=5*4*3-3*2*1=54