The digits \(1,2,3,4,5,6\) are written down in some order to form a sixdigit number.

(a) How many such six-digit numbers are there altogether?

(b) How many such numbers are even?

(c) How many are divisible by 4 ?

(d) How many are divisible by 8 ? (Hint: First show that the remainder on dividing a six-digit number \(a b c d e f\) by 8 is \(4 d+2 e+f\).)