How many $9$-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 $101$ or end with $11$ (or both)? Explain.
4. Have weight 5 and either start with 101 or end with 11 (or both)? Explain.