Discrete Math question I cant figure out how to do this I kn

Discrete Math question, I can\'t figure out how to do this, I know it involves C(n, k), but I don\'t know exactly how many times? Like C(n, k)*C(n-1,k). Anyways need help:
\"There are nine competitors in an Olympic ski trial from which the top three finishers advance. Of the nine, exactly 3 come from the USA. In how many (unordered) ways could at least two of the advancing competitors be from the USA? More importantly, describe your method using complete and grammatically correct sentences.\"

Solution

There are totally 9 ski divers. Of these 3 come from USA

Or it can be taken 6 non usa and 3 usa divers are there

OF these atleast 2 from USa to be taken for a group of 3.

Hence there can be either 2 Usa, 1 non usa or 3 usa

No of ways for 2 usa and 1 non usa = 3C26C1 = 18 ways

No of ways for 3 usa = 3c3 =1

Hence total no of ways = 18+1 =19