Question

В пространстве даны четыре точки, причем никакие три из них не лежат на одной прямой. Через каждые три из этих точек проводится плоскость. Сколько всего плоскостей получится? Решите и объясните пожалуйсто!

Answer 1

ОТВЕТ  ОТВЕТ  ОТВЕТ  ПОЛУЧИТСЯ  2

Answer 2

Problem Analysis

We are given four points in space, with no three of them lying on the same line. We need to determine the total number of planes that can be formed by selecting any three of these points.

Solution

To find the number of planes that can be formed, we can use the combination formula. The combination formula calculates the number of ways to choose a certain number of items from a larger set without regard to the order of the items.

In this case, we want to choose 3 points out of the 4 given points to form a plane. The combination formula for choosing r items from a set of n items is given by:

C(n, r) = n! / (r! * (n-r)!)

Where n! represents the factorial of n.

Let's calculate the number of planes that can be formed using this formula.

Calculation

Using the combination formula, we can calculate the number of planes that can be formed by choosing 3 points out of 4:

C(4, 3) = 4! / (3! * (4-3)!) = 4! / (3! * 1!) = 4

Therefore, a total of 4 planes can be formed by selecting any three points out of the given four points in space.

Conclusion

In conclusion, when given four points in space, with no three of them lying on the same line, a total of 4 planes can be formed by selecting any three points.