4. Consider bit strings with length l and weight k (so stringsof l 0’s and 1’s, including k 1’s). We know how to count the numberof these for a ?xed l and k. Now, we will count the number ofstrings for which the sum of the length and the weight is ?xed. Forexample, let’s count all the bit strings for which l + k = 11.

(a) Find examples of these strings of di?erent lengths. What isthe longest string possible? What is the shortest?

(b) How many strings are there of each of these lengths. Usethis to count the total number of strings (with sum 11).

(c) The other approach: Let n = l + p vary. How many stringshave sum n = 1? How many have sum n = 2? And so on. Find andexplain a recurrence relation for the sequence (an) which gives thenumber of strings with sum n.

(d) Describe what you have found above in terms of Pascal’sTriangle. What patter have you discovered?

I'd really appreciate the help on solving this problem as therewere no similar example problems in the book to even help me startthis problem. Thank you!

Also some background information on this problem to hopefullyhelp someone at least start answering this problem. For thisproblem we previously went over sequences such as recursive andclosed. Also if they were arithmetic or geometric. The last chapterdid cover binomial coefficients if that has some prevalencehere.