1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Y_Kistochka [10]
2 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 8x8 square grid. What is the probability that no two chosen squares share a row or a column?
Mathematics
1 answer:
erastova [34]2 years ago
7 0

Answer:

The probability is \frac{56!}{64!}

Step-by-step explanation:

We can divide the amount of favourable cases by the total amount of cases.

The total amount of cases is the total amount of ways to put 8 rooks on a chessboard. Since a chessboard has 64 squares, this number is the combinatorial number of 64 with 8, 64 \choose 8 .

For a favourable case, you need one rook on each column, and for each column the correspondent rook should be in a diferent row than the rest of the rooks. A favourable case can be represented by a bijective function  f : A \rightarrow A , with A = {1,2,3,4,5,6,7,8}. f(i) = j represents that the rook located in the column i is located in the row j.

Thus, the total of favourable cases is equal to the total amount of bijective functions between a set of 8 elements. This amount is 8!, because we have 8 possibilities for the first column, 7 for the second one, 6 on the third one, and so on.

We can conclude that the probability for 8 rooks not being able to capture themselves is

\frac{8!}{64 \choose 8} = \frac{8!}{\frac{64!}{8!56!}} = \frac{56!}{64!}

You might be interested in
Yesterday the snow was 2 feet deep in front of archies house. Today,the snow depth dropped to 1.6 feet because the day is so war
pshichka [43]

Answer:

20%

Step-by-step explanation:

becuz 2×.2 = .4

subtract .4 from 2 and it's 1.6 and change the .2 to percentage

3 0
3 years ago
It takes Emmanuel 20 minutes to walk to school. It takes Liah 80% as long to walk to school. How long does it take Liaqh to walk
77julia77 [94]

Answer:

16 minutes

Step-by-step explanation:

80% of 20 is

80/100 * 20 = 16

6 0
2 years ago
So, how do owls live. Like I need a serious explanation food,water,sleeping,predators,prey. Or give me all you know. But somethi
pashok25 [27]

<span>Owls are found in many different habitats, such as deserts, forests, prairies and even the Arctic tundra. They nest in trees, in holes in the ground, in barns, and in caves. And while many other birds migrate to warmer places during the winter, most owls do not. They live in the same place all year round.</span>
6 0
3 years ago
Read 2 more answers
Nina knows that the average of the x-intercepts represents the line of symmetry for a quadratic function through the x-axis. Whi
USPshnik [31]
I don't know for sure I'm going to ace grade next year but I know that you you need to put the coefficients with the same variable together and the variable next to the coefficients and multiply or add or divide or subtract them and you get your answer and this is just 7th grade math I'm relying on
4 0
3 years ago
Read 2 more answers
Point A and point B are placed on a number line. Point A is located at - 20 and
Igoryamba

Answer:

Point B is located on -25

4 0
3 years ago
Other questions:
  • Simplify 3 1/2 x 3 1/2
    15·1 answer
  • 7/10 = 350/x<br><br> Please help cross multiply
    11·1 answer
  • The cost of a pool cover depends on its area use the picture to find the area of the pool 30 50 25 10 5 40
    7·1 answer
  • One serving of pancakes takes one and two thirds cups of milk how many cups of milk will 36 servings of pancakes require?
    7·1 answer
  • I don't know how to use elimination without getting decimals when I divide to get like x's or y's The equation for elimination i
    13·1 answer
  • Given ln(y-4)=2t, solve for y
    7·1 answer
  • PLZ HELP!!!
    7·1 answer
  • A road crosses a railroad track at the top of a steep hill.The train cannot stop for oncoming cars, and cars cannot see the trai
    7·1 answer
  • 3. i) Determine the volume of the cylinder above to the nearest cubic centimetre. (3 points)​
    7·1 answer
  • Simplify the expression 2x(4 + x - 9 + 3x)
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!