How many [math]-bit strings (that is, bit strings of length 9) are there which:
  1. Start with the sub-string 101? Explain.
  2. Have weight 5 (i.e., contain exactly five 1’s) and start with the sub-string 101? Explain.
  3. Either start with [math] or end with [math] (or both)? Explain.
  4. Have weight 5 and either start with 101 or end with 11 (or both)? Explain.

Solution