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 is A, y us smaller/equal to 2 and y is smaller/equal to X
Answer:
See Below
Step-by-step explanation:
First, isolate x. To do that add 3.5 to each side
x - 3.5 = -3.1
+3.5 +3.5
x= 0.4
Answer:
1/3
Step-by-step explanation:
1 ÷ 3 = 1/3
1 divided by 3 is one-third, and one-third written as a fraction is 1/3.
Answer:
Cos^2x csc^2x
Step-by-step explanation:
Cos^2x (1 + cot^2x)