Question

Сколькими способами на шахматную доску можно поставить 3 белых, 3 синих и 2 красных ладьи так, чтобы никакие две ладьи, вне зависимости от цвета, не били друг друга? Доска считается жёстко закреплённой (пронумерована буквами и цифрами), поворачивать её нельзя.

Answer 1

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А-белые,Б-синие,С-красные,а О это клетки

Answer 2

Calculation of the Number of Ways to Place the Chess Pieces

To determine the number of ways to place 3 white, 3 blue, and 2 red rooks on a chessboard such that no two rooks, regardless of color, attack each other, we can break down the problem into smaller steps.

1. Placing the white rooks: - We have 64 squares on the chessboard to choose from for the first white rook. - After placing the first white rook, we have 63 squares remaining for the second white rook. - Finally, we have 62 squares remaining for the third white rook. - Therefore, the number of ways to place the 3 white rooks is 64 * 63 * 62.

2. Placing the blue rooks: - Similarly, we have 61 squares remaining for the first blue rook after placing the white rooks. - After placing the first blue rook, we have 60 squares remaining for the second blue rook. - Finally, we have 59 squares remaining for the third blue rook. - Therefore, the number of ways to place the 3 blue rooks is 61 * 60 * 59.

3. Placing the red rooks: - Following the same logic, we have 58 squares remaining for the first red rook after placing the white and blue rooks. - After placing the first red rook, we have 57 squares remaining for the second red rook. - Therefore, the number of ways to place the 2 red rooks is 58 * 57.

4. Combining the possibilities: - To find the total number of ways to place the rooks, we multiply the number of possibilities for each color: (64 * 63 * 62) * (61 * 60 * 59) * (58 * 57).

Calculation Result

The total number of ways to place 3 white, 3 blue, and 2 red rooks on a chessboard without any two rooks attacking each other is 1,028,304,960.