Question

How many different bit strings can be transmitted if the string begin with a 1 bit?

Answer 1

There are a total of 16 bits but we only need to worry about the last 13 since the first bit must be a 1 and followed by two zeros as such:

1 0 0 _ _ _ _  _ _ _ _  _ _ _ _  _

There are 3 more 1 bits followed by two zeros we must consider and the possible combinations are:

1 0 0      1 0 0    1 0 0    1 0 0    0 0 0 0

1 0 0      1 0 0    1 0 0    0 1 0    0 0 0 0

1 0 0      1 0 0    1 0 0    0 0 1    0 0 0 0

1 0 0      1 0 0    1 0 0    0 0 0    1 0 0 0

.....

.....

.....

and so on...

Since there are 13 bits to consider and 9 of those spots need to be arranged in the manner of a 1 bit followed by two 0 bits would the total possible number of combinations be C(13,9)