Here is a breakdown of the questions from the image:

1. Problem 1: There are six digits $1, 3, 4, 5, 7, 8$ to be arranged into a 3-digit odd number. The total number of odd numbers that can be arranged is:

   • A. 64
   • B. 112
   • C. 120
   • D. 144
   • E. 240

2. Problem 2: If mixing two different chemicals results in a new chemical, and there are six distinct chemicals available, how many new chemicals can be formed?

   • A. 12
   • B. 15
   • C. 20
   • D. 24
   • E. 32

3. Problem 3: From the digits $2, 3, 5, 6, 7, 9$, create 3-digit numbers that are less than 400. How many such numbers can be formed?

   • A. 10
   • B. 20
   • C. 40
   • D. 80
   • E. 120

4. Problem 4: A school is selecting a student council consisting of a president, vice president, and secretary. If there are 10 candidates, how many ways can the council be chosen?

   • A. 330 ways
   • B. 440 ways
   • C. 620 ways
   • D. 660 ways
   • E. 720 ways

5. Problem 5: From the digits $1, 2, 3, 4, 5, 6$, create 3-digit numbers that are less than 500. How many distinct numbers can be formed?

   • A. 80
   • B. 120
   • C. 150
   • D. 180
   • E. 200

6. Problem 6: From a group of 6 people, a team of 4 will be selected: one president, one secretary, and two members. How many different team configurations are possible?

   • A. 30
   • B. 80
   • C. 120
   • D. 210
   • E. 720

Would you like help with specific problems or explanations for how to solve any of them? Here are 5 questions to expand on the current problems:

1. How do you calculate the number of odd numbers formed from given digits?
2. What is the combination formula used to select 2 chemicals from 6?
3. How do restrictions like "less than 400" affect the total number of possibilities?
4. How are permutation principles applied to selecting a student council?
5. What changes if the team selection in problem 6 included different roles?

Tip: For any counting problems, always check if order matters (permutations) or if it does not (combinations).