Ask question

Ask question

All categories

2 years ago

6

How many ways are there to place 3 indistinguishable red chips, 3 indistinguishable blue chips, and 3 indistinguishable green ch

ips in the squares of a 3 x 3 grid so that no two chips of the same color are directly adjacent to each other, either vertically or horizontally?
A. 12,
B. 18,
C. 24,
D. 30 ,
E. 36

1 answer:

cricket20 [7]2 years ago

6 0

Answer:

E. 36

Step-by-step explanation:

Let:

$C_1 =$ color 1

$C_2 =$ color 2

$C_3 =$ color 3

Case I

C₂ C₃ C₂

C₃ C₁ C₃

C₁ C₂ C₁

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Case II

C₂ C₃ C₁

C₃ C₁ C₂

C₂ C₃ C₁

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Case III

C₁ C₃ C₂

C₂ C₁ C₃

C₃ C₂ C₁

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Case IV

C₂ C₃ C₁

C₃ C₁ C₂

C₁ C₂ C₃

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Case V

C₁ C₂ C₁

C₃ C₁ C₃

C₂ C₃ C₂

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Case VI

C₁ C₂ C₃

C₃ C₁ C₂

C₁ C₂ C₃

Since C₁ has 3 choices, then C₂ has 2 choices and C₁ has 1 choice

number of combinations = 3 × 2 × 1 = 6

Therefore, the total combinations = 6 + 6 + 6 + 6 + 6 + 6

= 36

You might be interested in

Which equation represents a function of x that is not linear?

AnnyKZ [126]

Answer:

y = 4x+3x^2

Step-by-step explanation:

For an equation to be linear, x must have a power of 1

y = 4x+3x^2 has a power of x that is not x ( x^2) so this is not linear ( it is quadratic)

8 0

3 years ago

HELP ILL GIVE A BRAINIEST

S_A_V [24]

Answer: The first one. 2 to the 20th power over 3 to the 8th power

Step-by-step explanation:

6 0

2 years ago

A store buys purses for $24.50 and then marks them up 25%. The store then discounts any purses that do not sell in the first mon

Sergeu [11.5K]

Answer:$27,57

1)find out how much wallets cost in the first month:

24,50 -100%

х - 125%

х= 24,50*125/100 ≈ 30,63

2)we will find out how much the wallets cost after the price is reduced by 10%:

30,63 - 100%

х -90%

х=30,63*90/100 ≈ 27,57

Step-by-step explanation:

3 0

3 years ago

Help math homework both questions

-Dominant- [34]

Answer:

Q-12 The vertical length of the top part of elevator to ground is 0.8484 meters .

Q -14 The glide runway path is 24,752.47 feet .

Step-by-step explanation:

Q - 12

Given as :

The diagonal length of the elevator = e = 1.2 meters

The vertical length of the top part of elevator to ground = x meters

The angle made by elevator with ground = Ф = 45°

<u>Now, According to figure</u>

Sin angle = $\dfrac{\textrm perpendicular}{\textrm hypotenuse}$

Or, Sin Ф = $\dfrac{\textrm x}{\textrm e}$

Or, Sin 45° = $\dfrac{\textrm x meters}{\textrm 1.2 meters}$

Or, 0.707 × 1.2 meters = x

∴ x = 0.8484 meters

So, The vertical length of the top part of elevator to ground = x = 0.8484 meters

Hence,The vertical length of the top part of elevator to ground is 0.8484 meters . Answer

Q-14

Given as:

The altitude of decent of plane = H = 10,000 feet

The angle of descend = Ф = 22°

Let the glide runway path = y feet

<u>Now, According to question</u>

Tan angle = $\dfrac{\textrm perpendicular}{\textrm base}$

Or, Tan Ф = $\dfrac{\textrm H}{\textrm y}$

Or, Tan 22° = $\dfrac{\textrm 10,000 feet}{\textrm y feet}$

Or, 0.4040 = $\dfrac{\textrm 10,000 feet}{\textrm y feet}$

Or, y = $\dfrac{\textrm 10,000 feet}{\textrm 0.4040}$

∴ y = 24,752.47

So,The glide runway path = y = 24,752.47 feet

Hence, The glide runway path is 24,752.47 feet . Answer

6 0

3 years ago

Scott collects hats. He has 65 hats an plans on buying 80 per year.

kicyunya [14]

Answer:

80x+65 2.465 3.865

Step-by-step explanation:

x being the number of years so in ten years he will have 80x10=800+65=865

80x5=400+65=465 so 5 is the number of years it would take

and i do not understand number 1 but i put a formula just in case that was it

7 0

3 years ago