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Placing of rooks

Source: Indian TST Day 3 Problem 3

July 11, 2014
combinatorics unsolvedcombinatorics

Problem Statement

In how many ways rooks can be placed on a 88 by 88 chess board such that every row and every column has at least one rook? (Any number of rooks are available,each square can have at most one rook and there is no relation of attacking between them)