Question

В университете обучается 903 студентов. Каждым из четырех видов спорта занимается по 215 студентов, каждыми двумя видами одновременно – по 46 студентов, каждыми тремя – по 9 студентов, всеми четырьмя – 3 студентов. Сколько студентов не занимается спортом?

Answer 1

Ответ:

если занимается спортом всего посчитать всех то выходит 273, то есть от 903 студентов отнимем 273 то выходит что 630 студентов не занимаются спортом

Answer 2

This is a mathematical problem that can be solved by using the inclusion-exclusion principle. The principle states that the number of elements in the union of several sets is equal to the sum of the number of elements in each set minus the sum of the number of elements in each pair of intersecting sets plus the sum of the number of elements in each triple of intersecting sets and so on.

In this problem, we have four sets: A, B, C and D, representing the four types of sports. We are given the number of students in each set and in each intersection of two, three or four sets. We want to find the number of students who are not in any of these sets, which is the same as the number of students in the complement of the union of these sets.

Using the inclusion-exclusion principle, we can write the following formula:

|A ∪ B ∪ C ∪ D| = |A| + |B| + |C| + |D| - |A ∩ B| - |A ∩ C| - |A ∩ D| - |B ∩ C| - |B ∩ D| - |C ∩ D| + |A ∩ B ∩ C| + |A ∩ B ∩ D| + |A ∩ C ∩ D| + |B ∩ C ∩ D| - |A ∩ B ∩ C ∩ D|

Substituting the given values, we get:

|A ∪ B ∪ C ∪ D| = 215 + 215 + 215 + 215 - 46 - 46 - 46 - 46 - 46 - 46 + 9 + 9 + 9 + 9 - 3

Simplifying, we get:

|A ∪ B ∪ C ∪ D| = 860 - 276 + 33 - 3

|A ∪ B ∪ C ∪ D| = 614

Therefore, the number of students who are in the union of the four sets is 614. To find the number of students who are not in any of these sets, we subtract this number from the total number of students in the university, which is 903. So, we get:

903 - 614 = 289

Hence, the answer is 289 students do not participate in any sport.