Question

Сколькими способами можно расположить 2 книги на 5 полках так, чтобы на каждой находилось не более одной книги? Помогите, пожалуйста!!!

Answer 1

10 разными способами. По умолчанию считаем, что книги одинаковые, т.е.  первая книга на верхней полке и вторая на нижней- это то же самое, что первая на нижней и вторая на верхней

Answer 2

Number of Ways to Arrange 2 Books on 5 Shelves

To determine the number of ways to arrange 2 books on 5 shelves, where each shelf can hold at most one book, we can use the concept of permutations.

The number of ways to arrange the books can be calculated by finding the number of permutations of 2 books taken from 5 shelves.

According to the search result from the number of permutations of 2 books taken from 5 shelves can be calculated using the formula:

P = n! / (n - r)!

Where: - n is the total number of shelves (5 in this case) - r is the number of books to be arranged (2 in this case) - ! denotes the factorial function

Using this formula, we can calculate the number of ways to arrange 2 books on 5 shelves:

P = 5! / (5 - 2)! = 5! / 3! = (5 * 4 * 3 * 2 * 1) / (3 * 2 * 1) = 120 / 6 = 20

Therefore, there are 20 ways to arrange 2 books on 5 shelves such that each shelf contains at most one book.

Please let me know if there's anything else I can help you with!