A keno round has three numbers in it. The size of the board, how many numbers the game draws, and how many you pick. Take a board of 40 numbers where the game draws 10, and call your picks spots. The chance that exactly m of your spots are hit is the count of ways that can happen divided by the count of all possible draws. In the usual notation it is C(k,m) multiplied by C(N-k, n-m), divided by C(N,n), where N is the board, n is the draw and k is your spot count.
That looks heavier than it is. On the 40-number board above, a single spot is hit 10 times in 40, which is 25%. With two spots, both are hit 5.77% of the time, exactly one is hit 38.46% of the time, and neither is hit 55.77% of the time. With three spots, all three come in 1.21% of the time, which is about one round in 82. With five spots, all five come in 0.038% of the time, about one round in 2,611. With ten spots, all ten come in once in 847,660,528 rounds.
One shortcut is worth carrying. On that board you hit a quarter of your spots on average, whatever your spot count is, because the draw covers a quarter of the numbers. Ten spots average two and a half hits. That average is the same for every configuration, which is why the paytable rather than the board decides what you are paid.
Board size and draw count vary between operators. Check both in the game rules before applying any figure from anywhere, including this page. The keno game page covers the variants in circulation.