A dec-string is a sequence of characters from the 10-character alphabet {0,1, 2,3, 4, 5, 6, 7, 8,9}. For example, these are dec-strings: 36562342320 49548362729 Let n >0 be an integer. 1. What is the number of dec-strings of length n? 2. What is the number of dec-strings d1,..., dn of length n such that dd2 + 00. In other words, what is the number of dec-strings of length n that don't begin with 00? 3. What is the number of dec-strings d1,..., d, of length n such that did2 # 00 and dzd + 11? 4. What is the number of dec-strings d1,..., dn of length n such that dd2 # 00 and dzd + 01? 5. What is the number of dec-strings d1,..., dn of lenght n such that did, = 00 or = 111? tp 6. What is the number of dec-strings d1,..., dn of length n > 4 such that dd2 # 00 or dzd + 11. 7. A dec-string d1,..., dn is bad if d; = d+1 or d; + di+1 = 9 for at least one i E {1,...,n 1} and it is good otherwise. What is the number of good dec-strings of length ? 8. A dec-string d1,..., dn is 2-bad if, d; = d; or d; +d; 9 for some i