Question

СРОСНО!!! МНОГО БАЛЛОВ!!!В ряду 14 кресел,на которых случайным образом рассаживают 3 юношей и 11 девушек. Найдите вероятность того,что юноши будут сидеть на трёх подряд идущих местах

Answer 1

Problem Analysis

We have a row of 14 chairs, and we need to find the probability that 3 boys will sit in three consecutive seats. There are a total of 14 seats, and we need to find the probability of a specific arrangement where the 3 boys are seated together.

Solution

To find the probability, we need to calculate the total number of possible arrangements and the number of favorable arrangements where the 3 boys are seated together.

The total number of possible arrangements can be calculated using the formula for permutations. Since there are 14 seats and 14 people, the total number of possible arrangements is 14!.

To calculate the number of favorable arrangements, we can treat the 3 boys as a single entity. So, we have 12 entities (11 girls + 1 group of 3 boys) to arrange in 12 seats. The number of favorable arrangements can be calculated using the formula for permutations. Therefore, the number of favorable arrangements is 12!.

Finally, we can calculate the probability by dividing the number of favorable arrangements by the total number of possible arrangements.

Let's calculate the probability:

Calculation

Total number of possible arrangements = 14!

Number of favorable arrangements = 12!

Probability = Number of favorable arrangements / Total number of possible arrangements

Result

The probability that the 3 boys will sit in three consecutive seats is (12! / 14!).

Please note that the exact numerical value of the probability cannot be determined without calculating the factorials.