Question

Найти вероятность того что из 10 книг случайным образом расставленных на полке 3 заданные окажутся рядом

Answer 1

Calculating the Probability of 3 Specific Books Being Together

To calculate the probability of 3 specific books being together out of 10 books randomly placed on a shelf, we can use the following approach:

1. Total Arrangements of 10 Books: - The total number of ways to arrange 10 books is given by 10 factorial (10!).

2. Arrangements of 3 Specific Books: - Since the 3 specific books must be together, we can consider them as a single entity. This reduces the problem to arranging 8 entities (3 specific books + 7 other books).

3. Calculating the Probability: - The probability of the 3 specific books being together is the ratio of the number of favorable arrangements to the total arrangements.

Calculation

The probability can be calculated using the following formula:

Probability = (Number of Favorable Arrangements) / (Total Arrangements)

The number of favorable arrangements can be calculated by considering the 3 specific books as a single entity and then arranging the 8 entities (3 specific books + 7 other books).

Result

The probability of the 3 specific books being together out of 10 books randomly placed on a shelf is (Number of Favorable Arrangements) / (Total Arrangements).

Let's calculate the probability using the provided information.