Problem of the Week
Problem E
Favourite Number 3

Matej told his friend Clare the following properties about his favourite number:

• It is a positive seven-digit integer.

• It contains each of the digits from \(1\) through \(7\) exactly once.

• The first digit is not \(1\).

• The second digit is not \(2\).

Clare then wrote down a number satisfying all these properties. What is the probability that the number Clare wrote was Matej’s favourite number?