how to calculate cascading game total events

Hi,
Does anyone know how to calculate cascading video game total events?
I did a simulation to list down the winning combination (cluster) hits, but I don't know how to calculate the total events( including both winning and non-winning combinations), so I can't calculate the probability of each winning cluster(combination)

it is a 4x5 grid ( 4 columns * 5 rows )
Symbol/Quantity
A/15
J/25
Q/25
K/25
cake1/10
cake2/10
Jackpot/10
Wild/9
scatter/5

Thanks

To calculate the total events for a cascading game on a 4x5 grid, use the multinomial coefficient formula:

𝑛!/(𝑛1!×𝑛2!×…×𝑛𝑘!)n!

Here, 𝑛 equals the total symbols (20), and 𝑛1,𝑛2,...,𝑛𝑘 are the quantities of each symbol you've listed. This will give you the total layouts, including both winning and non-winning combinations. Divide the number of winning combinations by this total to get the probability of each winning cluster.

thanks.
so the formula 𝑛!/(𝑛1!×𝑛2!×…×𝑛𝑘!)n! = 1/(𝑛1!×𝑛2!×…×𝑛𝑘!) ?

Quote: Molossus

To calculate the total events for a cascading game on a 4x5 grid, use the multinomial coefficient formula:

𝑛!/(𝑛1!×𝑛2!×…×𝑛𝑘!)n!

Here, 𝑛 equals the total symbols (20), and 𝑛1,𝑛2,...,𝑛𝑘 are the quantities of each symbol you've listed. This will give you the total layouts, including both winning and non-winning combinations. Divide the number of winning combinations by this total to get the probability of each winning cluster.
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