Problem Solving

M7MBA wrote:In how many ways can 3 different portraits be mounted on 3 of the four walls inside a room???

A) 4
B) 6
C) 12
D) 16
E) 24

The OA is the option E .

It shouldn't be 9? 3 walls and 3 portraits, 3*3=9. No? I need some help here. Thanks in advanced.

Hello M7MBA.

Let's see, we have:

- 4 walls from which we have to pick 3, it can be done as follows <i class="em em-point_down"></i> $$4C3\ =\frac{4!}{3!1!}=4\ different\ ways.$$

- We need to arrange 3 portraits, this can be done in 3! different ways, that is to say, 6 different ways.

Therefore, the number of ways that 3 different portraits can be mounted on 3 of the four walls inside a room is given by <i class="em em-point_down"></i> $$4\cdot3!=4\cdot6=24\ different\ ways.$$ This implies that the correct answer is the option E .

I hope it can help you. <i class="em em---1"></i>