A person wishes to visit $6$ cities, each exactly twice, and never visiting the same city twice in a row. In how many ways can this be done ?
I tried by inclusion exclusion.
But Having a problem in finding the total number of outcomes ?
I guess total number of outcomes can be found by using multinomial coefficients like $(12!)/(2!)(2!)(2!)(2!)(2!)(2!)$.
Am i proceeding correct ?