Question

Сколькими способами можно расставить 5 книг по алгебре 3 книги по геометрии и 2 по физике так, чтобы все книги по одному предмету стояли рядом

Answer 1

По условию получается, что нужна перестановка для 3. (алгебра, геометрия, физика)
Р₃=3!=1×2×3=6 способов.
Ответ: 6.

Answer 2

Calculation of the Number of Ways to Arrange the Books

To calculate the number of ways to arrange the books, we need to consider the books of each subject as a single entity. Therefore, we have three groups of books: algebra (5 books), geometry (3 books), and physics (2 books). We can arrange these three groups in any order, and within each group, the books can be arranged in different ways.

Let's calculate the number of ways to arrange the three groups first. We can arrange the three groups in 3! (3 factorial) ways, which is equal to 3 x 2 x 1 = 6.

Now, let's consider the arrangement within each group. For the algebra group, we have 5 books, so we can arrange them in 5! ways. Similarly, for the geometry group, we have 3 books, so we can arrange them in 3! ways. And for the physics group, we have 2 books, so we can arrange them in 2! ways.

Therefore, the total number of ways to arrange the books is calculated as follows:

Total number of ways = Number of ways to arrange the groups x Number of ways to arrange the books within each group Total number of ways = 6 x 5! x 3! x 2!

Let's calculate the result:

Total number of ways = 6 x 5! x 3! x 2! Total number of ways = 6 x 5 x 4 x 3 x 2 x 1 x 3 x 2 x 1 x 2 x 1 Total number of ways = 6 x 120 x 6 x 2 Total number of ways = 17280

Therefore, there are 17,280 ways to arrange the 5 books on algebra, 3 books on geometry, and 2 books on physics, such that all the books on the same subject are placed together.