Question

Пять студентов из группы изучают английский язык, шесть студентов – немецкий и семь студентов – французский язык. Случайным образом выбрано четыре студента. Какова вероятность того, что двое из них изучают английский язык, один изучает французский и один – немецкий?

Answer 1

$P= \frac{C_5^2\cdot C_6^1\cdot C_7^1}{C_{18}^4} = \frac{5\cdot 4\cdot 6\cdot 7}{2!\cdot 18\cdot 17\cdot 16\cdot 15} \approx 0,0057$

Answer 2

Probability Calculation for Language Study

To calculate the probability of randomly selecting four students, where two study English, one studies French, and one studies German, we can use the concept of combinations.

Given: - 5 students study English - 6 students study German - 7 students study French

The total number of students is 5 + 6 + 7 = 18.

The probability can be calculated using the formula: P = (C(n1, k1) * C(n2, k2) * C(n3, k3)) / C(N, n)

Where: - C(n, k) denotes the number of combinations of n items taken k at a time - n1, k1 = number of English students, number of combinations to choose 2 English students - n2, k2 = number of German students, number of combinations to choose 1 German student - n3, k3 = number of French students, number of combinations to choose 1 French student - N = total number of students - n = total number of students to be chosen

Let's calculate the probability using the given values.