Question

На скамейку в произвольном порядке садятся два мальчика и девочка из 6 "Б" класса. Какова вероятность того, что мальчики будут сидеть рядом?

Answer 1

Всего возможных вариантов 3!=6
Потом составляем комбинации из 2 мальчиков и девочки
Получиться ДмМ ДМм мДМ МДм мМД МмД 
Из 6 4 раскладки где мальчики сидят рядом⇒что вероятность равна 4/6=2/3

Answer 2

Probability of Boys Sitting Together on a Bench

To calculate the probability of the two boys sitting together on a bench, we need to determine the total number of possible seating arrangements and the number of arrangements where the boys are sitting together.

Given that there are two boys and one girl from the 6th grade class, we can assume that the three students will occupy three adjacent seats on the bench. The total number of possible seating arrangements can be calculated using the formula for permutations, which is n!, where n is the number of students.

In this case, n = 3, so the total number of possible seating arrangements is 3!.

To calculate the number of arrangements where the boys are sitting together, we can treat the two boys as a single entity. This means that we have two entities (the boys and the girl) that can be arranged in 2! ways. Additionally, the boys themselves can be arranged among themselves in 2! ways.

Therefore, the number of arrangements where the boys are sitting together is 2! * 2!.

To calculate the probability, we divide the number of arrangements where the boys are sitting together by the total number of possible seating arrangements:

Probability = (Number of arrangements where the boys are sitting together) / (Total number of possible seating arrangements)

Let's calculate the probability:

Number of arrangements where the boys are sitting together = 2! * 2! = 2 * 2 = 4

Total number of possible seating arrangements = 3!

Probability = 4 / 3!

Now, let's calculate the value of 3!:

3! = 3 * 2 * 1 = 6

Therefore, the probability of the boys sitting together is:

Probability = 4 / 6 = 2 / 3

So, the probability that the boys will sit together is 2/3.

Please note that the above calculation assumes that the bench has only three seats and that the students will sit in a specific order. If the bench has more than three seats or if the students can sit in any order, the calculation would be different.