Question

How many ways can 5 people be arranged in a line?

Answer 1

Answer: 120 ways

Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.

Let's start by drawing 5 blanks to represent the 5 different positions in the line.

Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have 5 4 3 2 1.

Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.

5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.

So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.

I have also shown my work on the whiteboard in the image attached.