Question 30
The digits of a positive five-digit number are 1, 2, 3, 4, 5 in some order. The first digit of the number is divisible by 1, the first two digits (in order) form a number divisible by 2, the first three digits (in order) form a number divisible by 3, the first four digits (in order) form a number divisible by 4, and the whole number is divisible by 5. How many such numbers are there?