Question

9 Реши задачу. Сколькими способами можно выложить в ряд два красных и два синих шарика? Шарики не отличаются ничем, кроме цвета. О ДОМАШНЕЕ ЗАДАНИЕ​

Answer 1

Ответ:

6

Пошаговое объяснение:

красных и 2 синих шариков ⇒ всего 4 шарика.

Количество перестановок всех шаров:

P₄=4!=1·2·3·4=24

2 красных и 2 синих шарики ⇒ всего 2 пары шаров разного цвета.

Количество перестановок двух пар шаров разного цвета:

P₄/(P₂·P₂)=24/(1·2·1·2)=6

Answer 2

Solving the Problem of Arranging Red and Blue Balls

To solve the problem of arranging two red and two blue balls in a row, we can use the concept of permutations.

Permutation Formula: The number of ways to arrange \( n \) objects is given by the formula \( n! \), where \( n! \) represents the factorial of \( n \).

Calculation

To calculate the number of ways to arrange two red and two blue balls, we can use the permutation formula for identical items. Since the red balls are identical to each other and the blue balls are identical to each other, we can use the formula for permutations of identical items, which is \( \frac{n!}{n_1! \cdot n_2! \cdot ... \cdot n_k!} \), where \( n \) is the total number of items, and \( n_1, n_2, ..., n_k \) are the counts of each type of identical item.

Applying the Formula

In this case, we have 4 balls in total (2 red and 2 blue), so the number of ways to arrange them is given by: \[ \frac{4!}{2! \cdot 2!} \]

Calculation

\[ \frac{4!}{2! \cdot 2!} = \frac{24}{2 \cdot 2} = 6 \]

Answer: So, there are 6 ways to arrange two red and two blue balls in a row.