Question

Из группы учащихся 26 человек Необходимо выбрать 2 главным дежурным одинаковыми обязанностями и 3 помощников. Сколькими способами это можно сделать?

Answer 1

Всего 5 дежурных а чел 26 26*5 =130 способов

Answer 2

Calculating the Number of Ways to Choose 2 Main Monitors and 3 Assistants

To calculate the number of ways to choose 2 main monitors and 3 assistants from a group of 26 students, we can use the combination formula.

The number of ways to choose r items from a set of n items is given by the combination formula:

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

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

Applying the Combination Formula

For this scenario: - n = 26 (total number of students) - r = 2 (number of main monitors to choose) - r = 3 (number of assistants to choose)

Using the combination formula, we can calculate the number of ways to choose 2 main monitors and 3 assistants from the group of 26 students.

Number of ways to choose 2 main monitors: C(26, 2) = 26! / (2! * (26-2)!) = 26! / (2! * 24!) = (26 * 25) / (2 * 1) = 325

Number of ways to choose 3 assistants: C(26, 3) = 26! / (3! * (26-3)!) = 26! / (3! * 23!) = (26 * 25 * 24) / (3 * 2 * 1) = 2600

Total Number of Ways

To find the total number of ways to choose 2 main monitors and 3 assistants, we multiply the number of ways to choose the main monitors by the number of ways to choose the assistants.

Total number of ways = 325 * 2600 = 845,000

Therefore, there are 845,000 ways to choose 2 main monitors and 3 assistants from a group of 26 students.