Let's solve each part of the question step by step.
### 1. Determine the number of boys and girls:
1. Number of Boys:
- Boys were assigned odd numbers.
- The total number of students is 15, and they are numbered from 1 to 15.
- Odd numbers within this range are: 1, 3, 5, 7, 9, 11, 13, 15.
- Therefore, there are 8 boys.
2. Number of Girls:
- Girls were assigned even numbers.
- Even numbers within this range are: 2, 4, 6, 8, 10, 12, 14.
- Therefore, there are 7 girls.
Summary:
- Number of Boys: 8
- Number of Girls: 7
### 2. Distance between the third and twelfth student:
- Each student stands 1 meter apart.
- The position numbers of the third and twelfth students are 3 and 12, respectively.
- To find the number of students between them, subtract the position of the third student from the position of the twelfth student: [tex]\( 12 - 3 \)[/tex].
- This gives us [tex]\( 9 \)[/tex] students between the third and twelfth students.
Distance:
- The distance is [tex]\( 9 \)[/tex] meters.
### 3. Pairs of students whose assigned numbers add up to 12:
- We need to find pairs of numbers between 1 and 15 that add up to 12.
- Let's list down all possible pairs:
- (1, 11)
- (2, 10)
- (3, 9)
- (4, 8)
- (5, 7)
- (6, 6) would not be a pair as it requires the same student to be counted twice.
Valid Pairs:
- (1, 11)
- (2, 10)
- (3, 9)
- (4, 8)
- (5, 7)
### Final Step-By-Step Solution Summary:
1. Number of Boys: 8
2. Number of Girls: 7
3. Distance between the third and twelfth students: 9 meters
4. Pairs of students whose assigned numbers add up to 12: [tex]\( (1, 11), (2, 10), (3, 9), (4, 8), (5, 7) \)[/tex]
Hence, we have successfully addressed all parts of the problem systematically.
