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Chapter 2: Q. 2.17 (page 49)

If 8rooks (castles) are randomly placed on a chessboard, compute the probability that none of the rooks can capture any of the others. That is, compute the probability that no row or file contains more than one rook.

Short Answer

Expert verified

8!648

Step by step solution

01

Given Information.

Let8rooks (castles) be randomly placed on a chessboard,

02

Explanation.

We go row by row.

First, we choose a position in a row 1from the 8columns for keeping the first rooks in 81the way.

Next, we choose a position in a row 2from the available 7columns(one column has been occupied by a rook1). This gives us71 choices.

Continuing like this, we get 8!ways to put the 8rooks on the chessboard given the conditions.

Total ways of keeping 8rooks on a chessboard are simple648.

03

Explanation.

8!648

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