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kenny6666 [7]
3 years ago
5

Eights rooks are placed randomly on a chess board. What is the probability that none of the rooks can capture any of the other r

ooks? Translation for those who are not familiar with chess: pick 8 unit squares at random from an 8 × 8 square grid. What is the probability that no two chosen squares share a row or a column? Hint. You can think of placing the rooks both with or without order, both ap- proaches work.
Mathematics
1 answer:
lbvjy [14]3 years ago
4 0

Answer:

4.51\times10^{-10}

Step-by-step explanation:

There are only 2 solutions for none of the rooks can capture any of the other rooks: only if they are laid out in either of the 2 diagonal of the chess board

The number of possible combination for the rock to laid out in 8x8 (64 slots) chess board

\frac{64 * 63 * 62 * 61 * 60 * 59 * 58 * 57}{8!} = \frac{1.78\times10^{14}}{40320} = 4426165368 possible combination

So the probability is pretty thin

P = 2 / 4426165368 = 4.51\times10^{-10}

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3 0
3 years ago
Read 2 more answers
The USS Enterprise was 1,123 feet in length.
Kitty [74]

Answer:

The scale for a model that is 30 inches long is 449.2 inches.

The scale for a model that is  2 feet long is 561.5 feet.

Step-by-step explanation:

Consider the provided information.

The USS Enterprise was 1,123 feet in length.

Part (A) What is the scale for a model that is 30 inches long?

1 feet = 12 inches.

First  convert the length of USS enterprise in inches.

1×1,123 feet = 12×1,123 inches

1,123 feet = 13476 inches

Divide original length with the length of model.

The scale for the model is:

\frac{13476}{30}=449.2\ inches

Hence, the scale for a model that is 30 inches long is 449.2 inches.

Part (B)  What is the scale for a model that is 2 feet long?

Since, both the units are in feet, so simply divide original length with the length of model.

The scale for the model is:

\frac{1123}{2}=561.5\ feet

Hence, the scale for a model that is  2 feet long is 561.5 feet.

6 0
3 years ago
Help me. The last person who answered this question just asked me for personal info.... so please just answer the question...
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Answer:

Step-by-step explanation:

so the least common denominator is 12, so:

multiply 3/4ab by three, which equals: 9/12ab

9/12ab-5/12ab = 4/12ab, or 1/3ab

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2 years ago
In the fraction below, which number is the numerator?<br> 3<br> 4<br> ।
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Answer: The 3 is the numerator.

The top number is always the numerator.

6 0
3 years ago
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3. Three years ago, Jane was three times as old as Alice. In two years time, the sum of their ages will be 62. Determine their p
anzhelika [568]
3 yrs ago:

Alice - x 
Jane - 3x 

Fast forward 2 years... 1 year ago: 

Sum of their ages = 62


Equation to solve: x + 3x = 62 
                                4x = 62 
                               -----  -----
                                 4      4
 
                                 x = 15.5 

From this, we can deterime that Alice is 15 1/2 years old. 

Then, plug in 15.5 for x in 3x to find Jane's age. 

15.5 × 3 = 46.5

From this, we can determine that Jane is 46 1/2 years old. 


I hope this helps you to understand this problem better.


5 0
3 years ago
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