Question

Команда из одинадцати футболистов разного роста случайным образом выстроилась в шеренгу.Найти вероятность того, что они стоят по ранжиру (то есть самый высокий стоит первым, и далее футболисты упорядочены по росту)

Answer 1

$\frac{1}{11!}$ =1/39916800

Answer 2

Probability of Football Players Standing in Height Order

To find the probability of a randomly arranged lineup of eleven football players standing in height order, we need to consider the total number of possible arrangements and the number of favorable arrangements where the players are ordered by height.

Let's break down the problem step by step:

1. Total Number of Arrangements: - Since the eleven football players have different heights, there are 11! (11 factorial) ways to arrange them in a line. This is because there are 11 choices for the first position, 10 choices for the second position, 9 choices for the third position, and so on, until there is only 1 choice for the last position. - Therefore, the total number of arrangements is 11! = 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1.

2. Number of Favorable Arrangements: - For the players to be arranged in height order, the tallest player must be in the first position, the second tallest player in the second position, and so on, until the shortest player is in the last position. - Since the players have different heights, there is only one favorable arrangement where they are ordered by height.

3. Probability Calculation: - The probability of an event is defined as the number of favorable outcomes divided by the number of possible outcomes. - In this case, the number of favorable arrangements is 1, and the number of total arrangements is 11!. - Therefore, the probability of the football players standing in height order is 1 / 11!.

Let's calculate the probability:

Probability = 1 / 11!

Now, let's evaluate this probability:

Probability = 1 / (11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)

Calculating this expression gives us the final probability.