Exercise 10.

Consider the bit strings in \(\B^6_2\) (bit strings of length 6 and weight 2).

  1. How many of those bit strings start with 1?

  2. How many of those bit strings start with 01?

  3. How many of those bit strings start with 001?

  4. Are there any other strings we have not counted yet? Which ones, and how many are there?

  5. How many bit strings are there total in \(\B^6_2\text{?}\)

  6. What binomial identity have you just given a combinatorial proof for?

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