Yes, try doing it like this,
using System;
using System.Diagnostics;
class ProcessStart{
    static void Main(string[] args){
        Process sample = new Process();
        sample.StartInfo.FileName   = "sample.exe";
        sample.Start();
    }
}
the key code is in the main function, just make sure the exe is in the same directory, and include the 
using System.Diagnostics; 
at the top.
this code works for me and seems the most correct way.
hope i helped.
    Process sample = new Process();
    sample.StartInfo.FileName   = "sample.exe";
    sample.Start();
just change the Process sample to w/e you want, so sample can be w/e you want.
you may also pass arguments to the exe using this.
sample.StartInfo.Arguments = "sample argument";
just put this before the starting the exe part.
hope i helped :)