Two variants of a test paper are distributed among 12 students. Number of ways of seating of the students in two rows so that the students sitting side by side do not have identical papers and those sitting in the same column have the same paper is :

Question

Two variants of a test paper are distributed among 12 students. Number of ways of seating of the students in two rows so that the students sitting side by side do not have identical papers and those sitting in the same column have the same paper is : (A) (12 !/6 ! 6 !) (B) ((12) !/25 ⋅ 6 !) (C) (6 !)2 ⋅ 2 (D) (6 !)2 ⋅ 22

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/b48188e0eaddbc2aed4e0d2dccc50dd1-.png" /> 6 students in column 1, 3, 5 have the same paper and those in 2, 4, 6 have the same paper. 6 such people of two sets can sit in 6 ! 6 ! ways and can interchange in 2 ways

Q. Two variants of a test paper are distributed among 12 students. Number of ways of seating of the students in two rows so that the students sitting side by side do not have identical papers and those sitting in the same column have the same paper is :

$\frac{12 !}{6 ! 6 !}$

$\frac{( 12 )!}{2 ^{5} \cdot 6 !}$

$(6!)^{2} \cdot 2$

$(6!)^{2} \cdot 2^{2}$

6 students in column 1, 3, 5 have the same paper and those in 2, 4, 6 have the same paper. 6 such people of two sets can sit in 6 ! 6 ! ways and can interchange in 2 ways

Q. Two variants of a test paper are distributed among 12 students. Number of ways of seating of the students in two rows so that the students sitting side by side do not have identical papers and those sitting in the same column have the same paper is :

6!6!12!​

25⋅6!(12)!​

(6!)2⋅2

(6!)2⋅22

6 students in column 1, 3, 5 have the same paper and those in 2, 4, 6 have the same paper. 6 such people of two sets can sit in 6 ! 6 ! ways and can interchange in 2 ways

$\frac{12 !}{6 ! 6 !}$

$\frac{( 12 )!}{2 ^{5} \cdot 6 !}$

$(6!)^{2} \cdot 2$

$(6!)^{2} \cdot 2^{2}$