How many different ways can a teacher line up 5 students for lunch?
You have 5 choices for the first in the lineup, 4 for the second, etc.
The total number of ways is the product of the different selection choices.
See also the contestant problem.
180
To find the number of different ways the teacher can line up 5 students for lunch, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
In this case, there are 5 students and we want to find the number of ways they can be lined up. Since order matters (the first student, second student, etc.), we use the formula for permutations:
P(n, r) = n! / (n - r)!
Where n is the total number of objects (students) and r is the number of objects in each arrangement (in this case, 5 students).
Using this formula:
P(5, 5) = 5! / (5 - 5)!
= 5! / 0!
= 5! / 1
= 5 x 4 x 3 x 2 x 1 / 1
= 120
Therefore, there are 120 different ways the teacher can line up 5 students for lunch.