Cardinality of permutations of 3 finite sets

I’m trying to understand the definition of the cardinality of permutations, but after looking online I’m still struggling with this:

If for example I have 3 finite sets:

$ A = \{2,2,4\}\$ $ B = \{1,2,3\}\$ $ C = \{4,5,1\}\$

And I want to find the cardinality of permutations, how should I do it? Does it mean to find the number of distinct permutations of each set and then multiply those 3 numbers? Can someone help me clarify the process? Thank you!