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B.Stat & B.Math 2022 - Q1

Source: Indian Statistical Institute (ISI) - B.Stat & B.Math Entrance 2022

May 8, 2022
isiIndian Statistical Institute2022combinatorics

Problem Statement

Consider a board having 2 rows and nn columns. Thus there are 2n2n cells in the board. Each cell is to be filled in by 00 or 11 .
[*] In how many ways can this be done such that each row sum and each column sum is even?
[*] In how many ways can this be done such that each row sum and each column sum is odd?