Daniellelillyonna959
Answered

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I really need help!!!
The kitchen, dining room, and living room of a house will be painted, each with a different color. There are 7 colors to choose from. This means that there are _[blank]_ color arrangements possible.

What number best completes the sentence?

Enter your answer as a number, like this: 42

Sagot :

elikasutton

Answer:

21

Step-by-step explanation:

First, you put all of the possiblities for the kitchen.

K1

K2

K3

K4

K5

K6

K7

Then, you multiply  7 by each room which would be 3 so,

3 * 7 = 21

So, 21 is probably your answer.

Lastly, have a great day!

MrRoyal

There are 210 color arrangements possible

The number of rooms (r) in the house is given as:

[tex]r = 3[/tex] ---- i.e. the kitchen, dining room, and living room

The number of available colors (n) to select from is also given as:

[tex]n = 7[/tex]

The possible color arrangement is calculated using the following permutation formula

[tex]^nP_r = \frac{n!}{(n - r)!}[/tex]

So, we have:

[tex]^7P_3 = \frac{7!}{(7 - 3)!}[/tex]

Remove bracket

[tex]^7P_3 = \frac{7!}{4!}[/tex]

Expand the numerator

[tex]^7P_3 = \frac{7 \times 6 \times 5 \times 4!}{4!}[/tex]

[tex]^7P_3 = 7 \times 6 \times 5[/tex]

[tex]^7P_3 = 210[/tex]

Hence, there are 210 color arrangements possible

Read more about permutation at:

https://brainly.com/question/11871015

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