isi-entrance 2022 Q1

isi-entrance · India · UGB Permutations & Arrangements Distribution of Objects into Bins/Groups

Consider a board having 2 rows and $n$ columns. Thus there are $2n$ cells in the board. Each cell is to be filled in by 0 or 1.
(a) In how many ways can this be done such that each row sum and each column sum is even?
(b) In how many ways can this be done such that each row sum and each column sum is odd?

Consider a board having 2 rows and $n$ columns. Thus there are $2n$ cells in the board. Each cell is to be filled in by 0 or 1.\\
(a) In how many ways can this be done such that each row sum and each column sum is even?\\
(b) In how many ways can this be done such that each row sum and each column sum is odd?

Paper Questions

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