To divide by a fraction, you can multiply by its inverse.
2 answers:
Answer:
Multiply and divide are inverse operations.
Multiply by a number is the same as divide by its reciprocal.
Step-by-step explanation:
To divide by a fraction, you can multiply by its inverse.
If a number is defined as a/b, then the reciprocal of the number is b/a.
The given equation is
Here, and
are inverse of each other.
Reason 1:
Multiply and divide are inverse operations.
Reason 2:
Multiply by a number is the same as divide by its reciprocal.
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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