B-I-N-G-O, statistics, combinatorics (?)

[JohnHale]

Hi,

So, I'm procrastinating making BINGO cards for my son's birthday party tomorrow. Star Wars-themed.So it's a 5x5 card. I have a pool of 37 images (yoda, boba fett, jar-jar binks (!), anakin, death star... etc.).How would I go about figuring out how many combinations there are? Actually I don't care about that, there's only 16 kids or so (I know it seems fishy since that 4 squared, but really). Oh, and one of the 37 images is the Star Wars logo and that's going to be on every single card; so there's a pool of 36 images and 24 empty spaces effectively, right?
Also, assuming the distribution to be appropriately random, and the images picked also to be random, what's the average number of turns I should expect a winner in? How often will there be two winners?Help my Observatory, you are my only hope.Is there an optimum or minimum number of pool of images for a given square?
These are mostly 7 year olds, so they don't really care, but I do want to avoid winner clashes. Obviously this won't be answered in time to help me (party's in about 13 hours), but I'm really curious.How would I solve this? Monte Carlo simulations?

Any help will be apprecited.

I didn't find the right solution from the Internet.

References:
arstechnica.com/civis/viewtopic.php?f=26&t=62266
Data Analysis Software Example

Thank you.

[Troy Coleman]

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[Rearldeen82]

Hi,

So, I'm procrastinating making BINGO cards for my son's birthday party tomorrow. Star Wars-themed.So it's a 5x5 card. I have a pool of 37 images (yoda, boba fett, jar-jar binks (!), anakin, death star... etc.).How would I go about figuring out how many combinations there are? Actually I don't care about that, there's only 16 kids or so (I know it seems fishy since that 4 squared, but really). Oh, and one of the 37 images is the Star Wars logo and that's going to be on every single card; so there's a pool of 36 images and 24 empty spaces effectively, right?
Also, assuming the distribution to be appropriately random, and the images picked also to be random, what's the average number of turns I should expect a winner in? How often will there be two winners?Help my Observatory, you are my only hope.Is there an optimum or minimum number of pool of images for a given square?
These are mostly 7 year olds, so they don't really care, but I do want to avoid winner clashes. Obviously this won't be answered in time to help me (party's in about 13 hours), but I'm really curious.How would I solve this? Monte Carlo simulations?

Any help will be apprecited.

I didn't find the right solution from the Internet.



Thank you.

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