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Printjmc
counting and probability intermediate
Problem
In Morse code, each symbol is represented by a sequence of dashes and dots. How many distinct symbols can be represented using sequences of 1, 2, 3, or 4 total dots and/or dashes?
Solution
We proceed by casework.
Case I: 1 dot or dash There are two possibilities: one dot, or one dash.
Case II: 2 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Case III: 3 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Case IV: 4 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Thus, there are distinct symbols that can be formed.
Case I: 1 dot or dash There are two possibilities: one dot, or one dash.
Case II: 2 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Case III: 3 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Case IV: 4 dots or dashes Each symbol can be a dot or a dash, so there are sequences in this case.
Thus, there are distinct symbols that can be formed.
Final answer
30