Question

Split 6 copies of one book, 7 copies of a second book, and 11 copies of a third book between two teachers, ensuring each teacher gets at least 2 copies of each book. Using generating function, the expression is:

a) (1+x2)⁶⋅(1+x²)⁷⋅(1+x²)¹¹
b) (1+x)⁶⋅(1+x)⁷⋅(1+x)¹¹
c) (1+x2)⁶⋅(1+x²)⁷⋅(1−x²)¹¹
d) (1−x)⁶⋅(1−x)⁷⋅(1−x)¹¹

Answer 1

The generating function for distributing 6, 7, and 11 copies of three books between two teachers, ensuring each receives at least 2 copies of each book, is represented by (a)
`\( (1 + x^2)^6 \cdot (1 + x^2)^7 \cdot (1 + x^2)^(11) \)`.

The generating function for distributing 6 copies of the first book, 7 copies of the second book, and 11 copies of the third book between two teachers with each receiving at least 2 copies of each book is expressed as
`\( (1 + x^2)^6 \cdot (1 + x^2)^7 \cdot (1 + x^2)^(11) \)`, which simplifies to
`\( (1 + x^2)^(24) \)`.

This formula accounts for the combinations of books each teacher receives, ensuring at least 2 copies of each book are distributed. The correct choice is (a)
`\( (1 + x^2)^6 \cdot (1 + x^2)^7 \cdot (1 + x^2)^(11) \)` in the given options.