Question

На полке 10 книг найти вероятность того что 4 книги поставлены рядом

Answer 1

$p= \frac{m}{n} = \frac{4!*6!}{10!} = \frac{1*2*3*4}{7*8*9*10} = \frac{1}{210}$

Answer 2

Calculating the Probability of 4 Books Being Placed Together on a Shelf

To calculate the probability of 4 books being placed together on a shelf out of 10 books, we can use the concept of permutations and combinations.

Permutations and Combinations

Permutations refer to the arrangement of objects in a specific order, while combinations refer to the selection of objects without considering the order.

Calculating the Total Number of Ways to Arrange 10 Books

The total number of ways to arrange 10 books can be calculated using the formula for permutations, which is given by: nPr = n! / (n - r)!

Where: - n is the total number of items - r is the number of items to be arranged - ! denotes factorial, which is the product of all positive integers up to that number

Using this formula, we can calculate the total number of ways to arrange 10 books.

Calculating the Number of Ways to Arrange 4 Books Together

To calculate the number of ways to arrange 4 books together, we can consider these 4 books as a single entity. This reduces the problem to arranging 7 entities (6 individual books + 1 group of 4 books).

The number of ways to arrange 7 entities can be calculated using the formula for permutations.

Calculating the Probability

Finally, the probability of 4 books being placed together can be calculated by dividing the number of ways to arrange 4 books together by the total number of ways to arrange 10 books.

Let's calculate the probability using the above approach.