Question

5. Ахрор, Сабит, Амина и Мастура купили всего 5 тетрадей. Если каждый из них взял хотя бы одну тетрадь, то сколькими способами можно распре- делить все тетради? Заполните таблицу: Ахрор Сабит Амина Мастура делайте решение понятно и составте условия ​

Answer 1

Ответ:

4•5=20 способов

Пошаговое объяснение:

Answer 2

To answer the question, let's break it down step by step.

Given Information:

- There are 5 notebooks in total. - Each person (Ahror, Sabit, Amina, and Mastura) took at least one notebook.

Approach:

To find the number of ways the notebooks can be divided among the four people, we can use a combinatorial approach. We need to distribute the 5 notebooks among the 4 people, ensuring that each person receives at least one notebook.

Solution:

To solve this problem, we can use the concept of "stars and bars." We can imagine the 5 notebooks as stars and the 4 people as bars. By placing the bars between the stars, we can divide the notebooks among the people.

Let's represent the stars as "o" and the bars as "|". We need to distribute the 5 notebooks among the 4 people, so we have 5 stars and 3 bars.

o o o o o | | |

Now, we need to count the number of ways we can arrange these stars and bars. This can be calculated using the formula for combinations with repetitions. The formula is:

C(n + k - 1, k - 1)

Where: - n is the number of stars (notebooks) - k is the number of bars (people)

In this case, n = 5 (notebooks) and k = 4 (people). Plugging these values into the formula, we get:

C(5 + 4 - 1, 4 - 1) = C(8, 3)

Using the formula for combinations, we can calculate this value as:

8! / (3! * (8 - 3)!) = 8! / (3! * 5!) = (8 * 7 * 6) / (3 * 2 * 1) = 56

Therefore, there are 56 ways to distribute the 5 notebooks among Ahror, Sabit, Amina, and Mastura, ensuring that each person receives at least one notebook.

Summary:

In summary, there are 56 ways to distribute the 5 notebooks among Ahror, Sabit, Amina, and Mastura, ensuring that each person receives at least one notebook. This can be calculated using the concept of "stars and bars" and the formula for combinations with repetitions.