There is a message that consists of 12 different symbols.This message is going to be sent through a transmition channel. The transmitter will additionally send 45 spaces between the symbols, with at least 3 spaces between each pair of symbols. In how many ways can the emitter send such a message?

My asnwer is: (using combinations with repetition)

$\displaystyle \frac{(11+12-1)!}{12!(11-1)!}. = 646,646

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