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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.