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The problem is/was formulated in a very bad style / (manner).
Actually, there are TWO DIFFERENT questions in it:
(a) the sequence in which the visits to the six selected cities are scheduled is also of concern.
It is unclear here to me if it is a question, at all . . .
(b) How many different sequences are there of six cities chosen from the total of 10 cities.
In my understanding, it is a typical case when the former English teacher tries to formulate a Math problem.
If you want to get an answer, then please formulate clearly your question/questions.