Entropy measurement from shuffled cards A standard deck of $52$ shuffled playing cards can be used as a source of randomness.

Assuming cards are not replaced as they're drawn, a full deck of cards provides $225.58$ bits of entropy $- 52!$ combinations $= \log_2(52!)$ bits of entropy.

What is the correct way to calculate the bits of entropy supplied by multiple decks of cards?

For a single deck reshuffled 3 times in a row I would expected $\log_2(52!^3) = 676.74$ bits. But for 3 decks shuffled together, what is the value?

Also, if $N$ cards have been drawn of $X$ decks, how much entropy has been accumulated?

This sounds like a homework question but I'm trying to develop this as a feature in a project - https://github.com/iancoleman/bip39/issues/33
Use the multinomial coefficients.