bash - 32 31 17 14 characters + length of X, Y and Z

Thanks to devnull for suggesting seq!

seq [X] [Y]|grep -c [Z] 

e.g. X = 100, Y = 200, Z = 20

$ seq 100 200|grep -c 20 2 

e.g. X = 100, Y = 200, Z = 10

$ seq 100 200|grep -c 10 11 

e.g. X = 0, Y = 1000000, Z = 2

$ seq 0 1000000|grep -c 2 468559