Discrete mathematics

1. How many Binary strings of length 6 do not start with zero?
2. Using only the digits { 1, 3, 5, 7, 9} how many three digit numbers can be formed under the following conditions:
   The first digit cannot be 3 or 9
   The second digit cannot match the first.
   The third digit has no restriction
3. How many natural numbers between 1 and 750, inclusive, are divisible by 4 or 7 but not both?
   SHow all calculation for your answer.
4. How many odd numbers in the range 100-599 have no repeated digits?
5. A focus group of 5 individuals is to be chosen from 26 vaccinated and 16 unvaccinated people.
   How many possible focus groups have exactly 3 vaccinated and 2 unvaccinated indiviuals?
6. How many different binary strings of length 15 have exactly 8 zeros?
7. On a test there are 6 multiple choice questions with 5 possible answers and 6 true-false questions. In how many ways can the 12 questions be answered (if none are to be left blank) ?
8. In how many ways can the letters from the set { a, b, c, d, e, f, g, h } be arranged if the letters 'f', 'g', 'h' must be adjacent to each other. (not necessarily in that order).

Sample Solution