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

E. 36

Step-by-step explanation:

Let:

color 1

color 2

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

where r the answers

step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1