1. Find the number of integers between 1 and 1000 that are not divisible by 5, 6, or 8. 2. a) In how many ways can you arrange 12 bits in a row such that there is exactly one substring of exactly five consecutive O's? b) In how many ways can you arrange 12 bits in a row such that there is exactly one substring of exactly five consecutive O's or one of exactly six consecutive 1's? 3. A nine digit identification number ABCDEFGHI is called a) neat if the digits satisfy A + B + C + D+E+F+G+H+I 80. How many different neat identification numbers are there? b) keen if A is equal to 5 or 6 and the product of the digits of the identification number is even. How many different keen identification numbers are there? c) cool if A + B +C+D+E+F+G + H+ I is odd. How many different cool identification numbers are there? d) brill if all of the digits alternate in parity and are distinct. How many different brill identification numbers are there?