In a certain country, vehicle registration plates consist of seven characters: a letter, followed by a three digit number, followed by three letters.

For example: B 474 PQR

The first letter cannot be a vowel; the three-digit number cannot begin with 0; and the first of the last three letters cannot be a vowel or any of the letters X, Y or Z.

a. Find the number of registration plates available.

b. Find the probability that a randomly selected registration plate is unassigned, given that there are 48.6 million vehicle owners in the country, and that each owns, on average, 1.183 registered vehicles.