I have read a few similar questions (see this question and this one), but cannot figure out how to adapt the solutions to fit my question. Unfortunately, my understanding of math is extremely limited, and I'm stumped by the number of factors influencing a result here.
I am creating modified BINGO game where players randomly write the numbers 1-42 (instead of 72, as it is normally played) on a 5x5 board (with a free space in the middle). Another change is that they would not write the numbers in order (e.g. the first row L-->R could be 1, 39, 12, 20, 17), and there are no limitations to which numbers can be placed in which rows.Therefore, any square could be any number--they just cannot write the same number twice on the board.
Like the regular (American) version, one letter and one number are drawn for each "call". "BINGO" can be 5 in a row horizontally, vertically, or diagonally.
If 10 people are playing (i.e. 10 boards), what would be the average number of draws it would take to get the first BINGO?
What would be the average number of draws if 20 people were playing?