Consider bit strings with length land weight k (so strings of l O's and l's, including k l's). We know how to count the number of these for a fixed l and Now, we will count the number of strings for which the sum of the length and the weight is fixed. For example, let's count all the bit strings for which l + k = 11 Find examples of these strings of diffe ent What ·s the longest string possible? What is the shortest? How .many strings are there of each of these Use this to count the total number of strmgs (with sum 11). The other approach: Let n = l + k How many strings have sum n = l? How many have sum n = 2? And so on.  Find and explain a recurrence relation for the sequence (an) which gives the number of strmgs with sum n. Describe what you have found abo e in terms of Pascal's What pattern have you discover,ed?

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