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The Telvio mobile service provider allows each customer to choose a part of their $10$- digit mobile number when getting a new connection. The first two digits of the number are fixed by the company based on the customer’s region. The customer can choose the last four digits as they wish. The company chooses each of the remaining four digits uniformly at random, and without replacement, from the list $\left \{ 0, 1, 2, \ldots,9 \right \}$. Note that this means that the digits in positions $3, 4, 5$ and $6$ in a Telvio number are all different.

What is the probability that in the mobile number assigned to a new customer by Telvio, the digits in positions $3, 4, 5$ and $6$ appear in increasing order when read from left to right?

  1. $\frac{1}{4}$

  2. $\frac{1}{16}$

  3. $\frac{1}{24}$

  4. $\frac{1}{32}$

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