Exercises 33 42 concern the set of binary strings of length 8 (each character is either the digit 0 or the digit 1). 33. How many such strings are there? 34. How many begin and end with 0? 35. How many begin or end with 0? 36. How many have 1 as the second digit? 37. How many begin with 111? 38. How many contain exactly one 0? 39. How many begin with 10 or have a 0 as the third digit? 40. How many are palindromes? (See Exercise 11.) 4. How many contain exactly seven Is? 42. How many contain two or more Os