The example starting at time 4:48 is incomprehensible to me. As far as I understand, for example, the cost of P1=CBADFE would be equal to 4+1+6+4+5 = 20, not 11. Also, I don't get why I don't see any closed path, for instance CBADFEC. Because he's talking about the Salesman's visiting cities problem, I would expect to see closed paths, indeed.