How many different symbols can be represented by in morse code, symbols are represented by variable-length sequences of dots and dashes. (for example, a=: -, 1 = sequences of six or fewer dots and dashes?

126 different symbols can be represented in Morse code

Step-by-step explanation:

We need to sum up the number of sequences using one single place, two places, three places, four places and so on until sequences of six places (dots and dashes).

For each case we use the fundamental counting principle.

For one single place we may have 2 possible sequences (a dash or a dot)

For two places (example: .. or ._) we may have 2*2 sequences, since each place may be filled with either dash or dot (2 possible ways) and then we multiply the ways each place can be filled, thus

Similarly, for three places we may have 2*2*2 sequences, thus

For four places we may have 2*2*2*2 sequences, thus

And so on.  

So, notice the total up to arrangements of six symbols, is:

23

step-by-step explanation: