Question

Из 20 студентов надо выбрать старосту, его заместителя и редактора газеты. Сколькими способами это можно сделать?

Answer 1

Здесь порядок имеет значение. То есть разными будут такие выборки

1- я выборка                                            2-я выборка

Иванов - староста                                     Иванов  - заместитель
Петров - Заместитель                               Петров  - редактор газеты   
Сидоров  - редактор газеты                      Сидоров - Староста 

Значит размещение

$A_{20}^3=\frac{20!}{3!}=$

=20*19*18*17*16*15*14*13*12*11*10*9*8*7*6*5*4=405483668029440000 способами

Ответ: 405483668029440000 способами

Answer 2

Problem Analysis

We need to select a president, vice president, and newspaper editor from a group of 20 students. We need to determine the number of ways this can be done.

Solution

To solve this problem, we can use the concept of combinations. Since the order of selection does not matter, we can use the combination formula to calculate the number of ways to select the positions.

The formula for combinations is given by:

C(n, r) = n! / (r! * (n-r)!)

Where: - n is the total number of items to choose from (in this case, the number of students) - r is the number of items to be chosen (in this case, 3 positions: president, vice president, and newspaper editor) - ! denotes the factorial operation, which is the product of all positive integers less than or equal to a given number

Let's calculate the number of ways to select the positions using this formula.

Calculation

Using the combination formula, we can calculate the number of ways to select the positions as follows:

C(20, 3) = 20! / (3! * (20-3)!)

Simplifying the equation:

C(20, 3) = 20! / (3! * 17!)

C(20, 3) = (20 * 19 * 18 * 17!) / (3! * 17!)

C(20, 3) = (20 * 19 * 18) / (3 * 2 * 1)

C(20, 3) = 1140

Therefore, there are 1140 ways to select the president, vice president, and newspaper editor from a group of 20 students.

Answer

There are 1140 ways to select the president, vice president, and newspaper editor from a group of 20 students.