Question

Answer Question 3 (3 points) Q5. If 11 students from a 1st-grade class are lining up to enter the cafeteria line for lunch, how many ways are there to line up the 11 students?

Answer 1

To find out how many ways 11 students can line up, we calculate the factorial of 11 (11!), which yields 39,916,800 different ways the students can be arranged in line.

Step-by-step explanation:

To determine how many ways there are to line up 11 students, we use the concept of a permutation. A permutation is an arrangement of all or part of a set of objects, with regard to the order of the arrangement.

Since we are lining up all 11 students without repeating, and the order matters, we calculate the total permutations using the formula for permutation of n distinct objects: n! (n factorial), where n is the number of objects to arrange.

Here, we have 11 students, so we calculate the factorial of 11:

11! = 11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1

This calculation gives us the total number of different ways the 11 students can line up for lunch.

Therefore, there are 39,916,800 different ways to line up the 11 students.