How many different ways can a teacher line up 5 students for lunch?
How many students are available to chose among? Does the order in which they are lined up matter?
If the answers are Five and Yes, the answer is 5! = 5x4x3x2x1 = 120
120
To determine the number of different ways a teacher can line up 5 students for lunch, we can use the concept of permutations.
Permutations calculate the number of ways objects can be arranged in a specific order. In this case, we want to find the number of ways the 5 students can be arranged in a line for lunch, where the order matters.
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where:
n is the total number of objects (students in this case)
r is the number of objects to be selected (the number of students in the line)
! denotes factorial, which is the product of all positive integers from 1 to n
Now let's calculate the permutations for the given scenario:
P(5, 5) = 5! / (5 - 5)!
= 5! / 0!
= 5! / 1
= 5 x 4 x 3 x 2 x 1 / 1
= 120 / 1
= 120
Therefore, there are 120 different ways a teacher can line up 5 students for lunch.