How many different ways can 25 students line up for lunch?

Step-by-step explanation:

We are asked to find the number of ways 25 students line up for lunch.

Since there are 25 students, so the students for the 1st place can be chosen in 25 ways.

As 1 student is already chosen for 1st place and there are 24 students left, so the students for the 2nd place can be chosen in 24 ways.  

Since 2 students are already chosen and there are 23 students left, so the students for the 3rd place can be chosen in 23 ways.

We will continue this process till we fill all the 25 places.

We can represent as , therefore, 25 students can be line up for lunch in different ways.