Question

how many ways are there to split 6 copies of one book, 7 copies of a second book and 11 copies of third book two teachers if each teacher gets 12 books and each teacher gets at least 2 copies of each book?

Answer 1

There are 225 ways to split the books among the two teachers.

Step-by-step explanation:

To determine the number of ways to split the books among the two teachers, we can use the concept of combinations. First, we need to distribute 12 books to each teacher, while ensuring that each teacher gets at least 2 copies of each book.

Let's consider the first book. Teacher 1 must receive at least 2 copies, which leaves 4 copies for Teacher 2. We can distribute these 4 copies in 5 ways.

Similarly, for the second book, there are again 5 ways to distribute the remaining 5 copies. Finally, for the third book, we have 9 ways to distribute the remaining 9 copies. To find the total number of ways, we multiply the number of ways for each book together: 5 x 5 x 9 = 225 ways.