A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule. The underlying principle that they are working on is the following: Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.

If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is:

The correct option is C.

Let the 10 cities be denoted as $C_1,C_2,...,C_{10}$.

According to the underlying principle, a person staying in any city $C_i$ must be able to:
1. Make a trip to any other city $C_j$ in the morning.
2. Return from $C_j$ back to $C_i$ by the evening of the same day.

Since the journey between any two cities must be performed using only direct (non-stop) flights, this implies:
• There must be a direct flight from $C_i$ to $C_j$ in the morning.
• There must be a direct flight from $C_j$ to $C_i$ in the evening.

Since this must be possible for every pair of cities $(C_i,C_j)$:
• The number of directed connections needed is equal to the number of ordered pairs of cities.
• With $n=10$ cities, the number of ordered pairs is:
$P=n(n-1)=10\times 9=90$
Therefore, the minimum number of direct flights that need to be scheduled is 90.