1. Find the number of integers between 1 and 1000 that are not divisible by 5,...

   

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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? 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?