The question follows:
"In a lottery game $6$ balls are drawn randomly from $49$ balls. If you pick $6$ different numbers:
i) What is the probability that your numbers match those drawn?
ii) What is the probability that exactly $x$ of the numbers you choose match?"
So I've done part (i) and got $$\frac{1}{\binom{49}{6}}$$ which is roughly $7.2E-10$, but I'm not sure on how to approach (ii).
Your answer to the first question is correct.
Hint: If you match exactly $x$ of the $6$ selected numbers, you must also choose $6 - x$ of the remaining $49 - 6 = 43$ numbers.