Question

В коробке семь одинаковых пронумерованных кубиков. Наудачу извлекают все кубики по очереди. Найти вероятность того, что номера кубиков появятся в убывающем порядке.

Answer 1

Это c из n по k (n снизу, k сверху от c);
События зависят друг от друга (поэтому c, а не a); это произведение вероятностей.
Вероятность вытащить 1 кубик с номером 7:
1/7
Вероятность вытащить второй кубик с номером 6 (p.s. нам важна последовательность, поэтому номера кубам для красоты даю):
1/6

И т.д,; получается: 1/7*1/6*1/5*1/4*1/3*1/2*1/1= лень считать :)

Answer 2

Problem Analysis

We are given a box containing seven identical numbered cubes. The cubes are extracted randomly one by one. We need to find the probability that the numbers on the cubes appear in descending order.

Solution

To find the probability, we need to determine the total number of possible outcomes and the number of favorable outcomes.

# Total Number of Outcomes

The total number of outcomes is the total number of ways the cubes can be arranged. Since there are seven cubes, each with a unique number, there are 7! (7 factorial) ways to arrange them.

Therefore, the total number of outcomes is 7!.

# Number of Favorable Outcomes

To find the number of favorable outcomes, we need to determine the number of ways the cubes can be arranged in descending order.

Since the cubes are numbered, we can assign the numbers 1 to 7 to the cubes in descending order. The first cube can have any number from 1 to 7, the second cube can have any number from 1 to the number on the first cube, and so on.

Therefore, the number of favorable outcomes is the number of ways to choose 7 numbers from 1 to 7 in descending order. This can be calculated using the formula for combinations:

Number of favorable outcomes = C(7, 7) = 1

# Probability

The probability is the ratio of the number of favorable outcomes to the total number of outcomes:

Probability = Number of favorable outcomes / Total number of outcomes

Substituting the values we calculated:

Probability = 1 / 7!

Simplifying further:

Probability = 1 / (7 x 6 x 5 x 4 x 3 x 2 x 1)

Calculating the value:

Probability = 1 / 5040

Therefore, the probability that the numbers on the cubes will appear in descending order is 1/5040.