This is not a permutation. It's a combination. The order the countries are picked in do not matter. That is, if I'm selecting 9 from 70 countries, it won't matter if I pick country A first followed by country B, or country B first followed by country A. They will still be A and B either way. Therefore, order does not matter. And for picking 1, it doesn't really matter anyway.
What does matter is separating the 3 parts, and doing each part individually. The answers for each part will be multiplied together for a final answer.
There's 51 ways to pick 1 out of 51. That will always be the case if you're only picking 1, but doing the math:
C(51,1) = 51!
which does = 51
Likewise, there's 68 ways to pick 1 from 68, just like above.
Then you do C(70,9) = 70! / [9!(70-9)!]
(If you're having trouble working those out, just say so.)
Then the answers to each of those 3 are multiplied. One way to know they're multiplied is the whole thing is "and"s. That is, we pick the 1 and we pick the 1 and we pick the 9. So it's like "continuing down the line" doing picking. It's just that the first pick came from a pool of 51, and the next pick came from a pool of 68, and the next 9 picks all came from a pool of 70.