Combinatorics Problem with symbols and spaces Here is my problem that I have to solve:
An agent will send a secret code made up of 12 different symbols across a secure
wire. In addition to the 12 symbols, the agent will also send a total of 45 blank spaces between the symbols, with at least three spaces between each pair of
consecutive symbols. How many ways are there for the agent to send such a
message?
Just the wording of this problem has me thoroughly confused and lost.
Now, I figure that since the agent will put at least 3 spaces between a pair of consecutive symbols, then at least 36 spaces would be used. But that's all I have figured out, if I even did that correctly.
Could someone help me solve this problem?
Thank you for any help.

You have $12$ symbols, so there are $11$ gaps between them.  Each gap has to have at least $3$ spaces, so we have accounted for $33$ spaces.  Your question is then the number of ways to distribute the remaining $12$ spaces between the gaps.  This is the number of weak compositions of $12$ into $11$ parts, which you can solve by a stars and bars argument.  You also need to assess how many choices there are for the message.
