# Expected time to visit all countries by random flight paths [closed]

Say there are $$n$$ different countries, the flight starts from some initial country. At each step, the flight can go to a random country other than the one where it currently is. The probability of going to other countries are equal. Let random variable $$X$$ be the number of steps until the flight has visited all the countries at least once. What is $$\mathbb{E}[X]$$?

I drew some examples and got $$1/(n-1)^n$$, but I don't know what to do next. I think it needs linearity of expectations.