Problem 3 (Counting binary strings) 20 marks/ Consider all bit strings of length 15. 1. How many ...

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Problem 3 (Counting binary strings) 20 marks/ Consider all bit strings of length 15. 1. How many begin with 00? 2. How many b

Answer 1

Answer #1

Each bit in the 15 bit string can take 2 possible values (0 and 1)

1. Number of strings starting with 00 = 2¹³ = 8192

2. Number of strings starting with 00 and end with 11 = 2¹¹ = 2048

3. Begin with 00 or end with 11 = begin with 00 + end with 11 - begin with 00 and end with 11 = 2¹³ +2¹³ -2¹¹ =14336

4. Exactly 10 1's = 15C10 = 3003

We solve only 4 questions in one post. Please post again for other solutions.

Answer 2

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