In game, we randomly generate four grids (cards) $3\times 5$ (row × col), with each column containing 3 numbers randomly selected without replacement from 18 possibilities: first columns from the left are randomly selected from the numbers 1-18, the second columns are selected from 19-36, the third column from 37-54, the fourth columns from 55-72, and the fifth columns from 73-90.
So, for the first columns we fill in 3*4=12 different numbers from the 1-19 without replacement, and so on. Please, see image.
Then, we randomly draw, without replacement, from a pool of balls numbered 1 through 90, 40 balls at ones.
Please find winning patterns on the top of image.
Question is how to calculate the probability, for example, of the event on the attached image. You can see, that the second grid won on two patterns: 8 + 3, and also we have single wins on the first and fourth grids.
I’m kindly asking to show me how to calculate these probabilities. In fact, I need to calculate the expected win in that game. So, basically I need to cover up all outcomes.