Question

В классе 21 учащийся, среди них два друга- Вадим и Олег.Класс случайным образом разбивают на 3 равные группы. Найдите вероятность того, что Вадим и Олег окажутся в одной группе.

Answer 1

Вероятность 1/7,..........

Answer 2

Calculating the Probability of Vadim and Oleg Being in the Same Group

To calculate the probability of Vadim and Oleg being in the same group when the class is randomly divided into 3 equal groups, we can use the following approach:

1. Total Number of Ways to Divide the Class into 3 Groups: - The total number of ways to divide a class of 21 students into 3 equal groups can be calculated using the formula for combinations, which is given by nCr = n! / (r! * (n-r)!), where n is the total number of students and r is the number of students in each group.

2. Number of Ways Vadim and Oleg Can Be in the Same Group: - We need to calculate the number of ways Vadim and Oleg can be in the same group when the class is divided into 3 equal groups.

3. Calculating the Probability: - Finally, we can calculate the probability of Vadim and Oleg being in the same group by dividing the number of favorable outcomes (i.e., the number of ways Vadim and Oleg can be in the same group) by the total number of ways to divide the class into 3 groups.

Let's proceed with the calculations using the provided information.

Total Number of Ways to Divide the Class into 3 Groups

The total number of ways to divide a class of 21 students into 3 equal groups can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

Using this formula, we can calculate the total number of ways to divide the class into 3 groups.

Number of Ways Vadim and Oleg Can Be in the Same Group

We need to calculate the number of ways Vadim and Oleg can be in the same group when the class is divided into 3 equal groups.

Calculating the Probability

Finally, we can calculate the probability of Vadim and Oleg being in the same group by dividing the number of favorable outcomes by the total number of ways to divide the class into 3 groups.

Let's proceed with the calculations.