Question

Сколькими способами можно посадить в ряд 4 пары близнецов так, чтобы никакие 2 близнеца не сидели рядом?

Answer 1

1сп. 1212
2сп. 2121
только 2 способа.

Answer 2

Calculating the Number of Ways to Seat Twin Pairs

To calculate the number of ways to seat 4 pairs of twins in a row so that no two twins are sitting next to each other, we can use the concept of permutations.

Step 1: Arrange the Non-Twin Seats

First, we arrange the non-twin seats. Since twins cannot sit next to each other, we treat each pair of twins as a single entity. This means we have 5 entities to arrange: 4 non-twin entities and 4 twin entities.

Step 2: Arrange the Twin Pairs

Next, we arrange the twin pairs within the available spaces. Since there are 5 entities to arrange, there are 5! (5 factorial) ways to arrange them.

Step 3: Account for the Arrangements within Twin Pairs

Within each twin pair, there are 2 ways to arrange the twins.

Calculation

Using the steps above, the total number of ways to seat 4 pairs of twins in a row so that no two twins are sitting next to each other can be calculated as follows:

Total arrangements = (Number of ways to arrange non-twin entities) * (Number of ways to arrange twin pairs) * (Number of ways to arrange within twin pairs)

Total arrangements = 4! * 5! * (2^4)

Final Answer

By substituting the values and calculating the expression, we can determine the total number of ways to seat 4 pairs of twins in a row so that no two twins are sitting next to each other.

Total arrangements = 24 * 120 * 16 = 46080

Therefore, there are 46080 ways to seat 4 pairs of twins in a row so that no two twins are sitting next to each other.