Need help finding an algorithm to find a subset of an array

I am not able to come up with an algorith for this. Please help me.
There is an array string []arServiceNames. Let nServices be the size of this array.

There is a structure
struct Service
{
string name;
DateTime startDateTime;
DateTime endDateTime;
}

There is an array Service[]arAppointments of this structure. The elements of this array are sorted in the ascending order of startDateTime.
I need to write a program which will find a subset of arAppointments. Let the subset be arScheduledAppointments.

arScheduledAppointments should satisfy the following conditions:-
1. Number of its elements = nServices
2. arScheduledAppoinments[i].name = arServices[i] for any value of i from 0 to nServices-1
3. The startTime of an element of this array should be equal to or more than endTime of the previous element but if it is more then the difference should be maximum 15 minutes (not more). In other words, when one service finishes then the next should start within 15 minutes.

Let me know how to do it. Complete program is not needed. Just let me know some efficient algorithm to achieve this.
The number of elements in arAppointments can go up to 300 but the number of elements in arServices is quite small (5 at most).
Thanks.

To find a subset of an array, use Array.FindAll function like this:

Code:

---

        static void Main(string[] args)
        {
                        string[] countries = new string[] {"India", "Singapore", "Canada", "USA"};
            string[] interestingOnes = Array.FindAll(countries, (country) => country.Equals("Canada"));
            foreach(string country in interestingOnes)
            {
                Console.WriteLine(country);
            }
        }

---

Sorry but my question is different.