In how many ways can 8 students be placed on a line?


To determine how many ways 8 students can be placed in a line, we calculate the number of permutations of 8 distinct students. This can be found using the factorial function, represented as \( 8! \).

\[
8! = 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 40,320
\]

Thus, there are **40,320 ways** to arrange 8 students in a line.

Would you like more details or further explanation on this? Here are 5 related questions:

1. How many ways can 5 students be arranged in a circle?
2. What is the number of ways to arrange 10 students in a line if 2 of them must always sit next to each other?
3. How many ways can 3 students be chosen from a group of 8 for a task?
4. In how many ways can you arrange 8 students in a line if one student must always be first?
5. How many ways can 8 students be seated in a line if two specific students cannot sit next to each other?

**Tip:** The factorial function grows very quickly, so for large numbers, approximate methods or algorithms are often used to calculate them efficiently.

In how many ways can 8 students be placed on a line?

Find out how many ways 8 students can be arranged in a line using the factorial formula. This problem introduces permutations and factorials, perfect for students in Grades 9-12. The solution calculates 8! = 40,320 ways to arrange the students.

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