Answer:
The probability is 
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,
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
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

Answer:


The interval notation is: 
Step-by-step explanation:



Answer:
Basic college math topics include whole numbers, fractions, numbers, decimals and integers. Problem solving, algebra, percents and geometry are also included in course content.
Step-by-step explanation:
Answer:
x = 7
42, 35, 7
Step-by-step explanation:
- EG = 5x+7
- EF = 5x
- FG = 2x-7
Point F is on line segment of EG, therefore EG = EF + FG
- 5x + 7 = 5x + 2x - 7
- 2x = 14
- x = 7
Then
- EG = 5*7 + 7 = 42
- EF = 5*7 = 35
- FG = 2*7 - 7 = 7