Question

One room in a house will get new carpeting, drapes, and paint. There is a choice of 4 carpets, 6 drapes, and 3 colors of paint. How many different ways can this room be decorated?

a) 72 ways
b) 72 colors
c) 144 ways
d) 144 colors

Answer 1

To determine the number of different ways to decorate the room, we multiply the choices of carpets (4), drapes (6), and paint (3) according to the fundamental counting principle, resulting in 72 different ways to decorate the room (option a).

Step-by-step explanation:

The subject of this question is Mathematics, and it seems suitable for a Middle School grade level. The question asks how many different ways a room can be decorated given the choices available for carpets, drapes, and paint. To answer this, we use the fundamental counting principle which states that if there are n ways to do one thing, and m ways to do another thing after that, then there are n * m ways to do both.

Therefore, the number of ways to decorate the room is the product of the number of choices for each item. In this case, there are 4 choices for carpets, 6 choices for drapes, and 3 choices for paint. Multiplying these numbers together:

Number of ways = 4 (carpets) * 6 (drapes) * 3 (paint) = 24 * 3 = 72 ways.

So, the room can be decorated in 72 different ways, which corresponds to option a) 72 ways.