A network administrator needs to assign temporary passwords to users. This is done by assigning a 10-digit password which contains each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 exactly once. However, to prevent just any such password, there are some that will fail. Those that will fail are those that contain the following sequence of numbers "30459", "304521", and "1768". For example, 0123456789 is allowed but neither 0176823459 nor 3045217689 are allowed.
How many passwords contain 30459 and 1768?