Question

Avani has 5 posters she wants to hang on the wall. How many different ways can the posters be arranged in a row?​

Answer 1

Answer:

15 ways

Step-by-step explanation:

The first can be in 5 spots

The second can be in 4 spots.

The third can be in 3 spots.

The fourth can be in 2 spots.

The fifth can be in 1 spot.

The sum of all of the numbers is 15.

5 + 4 + 3 + 2 + 1 = 15

Answer 2

Given ↓

• Avani has 5 posters

To Find ↓

• The number of ways Avani can arrange her 5 posters

Calculations ↓

First, how many ways are there for the 1st poster?

It can be the first, the 2nd, the 3rd, the 4th, or the 5th.

How many ways are there for the 2nd poster?

there are 4 ways, because one of them is occupied by the first poster

There are 3 ways for the 3rd poster, 2 ways for the 4th poster and 1 way for the 5th poster.

Multiply the number of ways together : 120 ways

These are the ways we can arrange the 5 posters ↓

$\boxed{\\\begin{minipage}{2 cm}poster~1 \\ \\ \end{minipage}}$     $\boxed{\\\begin{minipage}{2cm}poster~2 \\ \\ \end{minipage}}$   $\boxed{\\\begin{minipage}{2cm}poster~3 \\ \\ \end{minipage}}$  $\boxed{\\\begin{minipage}{2cm}poster~4 \\ \\ \end{minipage}}$  $\boxed{\\\begin{minipage}{2cm}poster~5 \\ \\ \end{minipage}}$

We could replace P1 (Poster 1) with any of the 4 posters here, and do the same thing with the other posters...

Overall, believe it or not, there are 120 ways to arrange these 5 posters.

A quick way to calculate this is

5!=5*4*3*2*1

120

Number of ways ↓

120

hope helpful ~