Question

What is the number of ways in which one can colour the squares of a 4 × 4 chessboard with colours red and blue such that each row as well as each column has exactly two red squares and two blue squares?

Answer 1

Number of ways of arranging 2R and 2B in 1st row

In the first column the remaining entries can be filled in 3 ways.

In the column in which the element in (1, 1) position repeats in first row, we can fill in 3 way (1 + 2)