Question

Помогите пожалуйста с решением! Задачи: Сколькими способами можно составить семейную пару из 7 юношей и 5 девушек? И ЕЩЕ ОДНА Из 10 журналистов одной газеты требуется выбрать четырёх для ведения тематических страничек: «Спорт», «Новости дня», «Красота», «Здоровье». Сколькими способами это можно сделать?

Answer 1

Пара состоит из юноши и девушки. юношу можно выбрать 7-ю способами, девушку 5-ю. вероятности перемножаются.
7*5=35 способами.
из 10 журналистов надо выбрать 4-х, что бы вели разные странички.
Первого 10ю сп, второго 9ю, третего 8ю, четвертого 7:
10*9*8*7=6230 способов.

Answer 2

Combinations and Permutations

To solve the first problem, we need to determine the number of ways we can form a family pair from 7 boys and 5 girls. This can be solved using combinations.

The formula for combinations is given by:

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

Where: - n is the total number of objects to choose from - r is the number of objects to choose

In this case, we want to choose 1 boy and 1 girl to form a family pair. So, n = 7 (number of boys) and r = 1 (number of boys to choose). Similarly, n = 5 (number of girls) and r = 1 (number of girls to choose).

Using the combination formula, we can calculate the number of ways to form a family pair:

Number of ways = C(7, 1) * C(5, 1)

Let's calculate this:

Number of ways = (7! / (1!(7-1)!)) * (5! / (1!(5-1)!))

Number of ways = (7! / (1! * 6!)) * (5! / (1! * 4!))

Number of ways = (7 * 6 * 5 * 4 * 3 * 2 * 1) / ((1 * 6 * 5 * 4 * 3 * 2 * 1) * (1 * 4 * 3 * 2 * 1))

Number of ways = 7 * 5 = 35

Therefore, there are 35 ways to form a family pair from 7 boys and 5 girls.

Moving on to the second problem, we need to determine the number of ways we can choose 4 journalists from a group of 10 for the thematic pages.

This can be solved using combinations as well. The formula remains the same:

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

In this case, we want to choose 4 journalists from a group of 10. So, n = 10 (total number of journalists) and r = 4 (number of journalists to choose).

Using the combination formula, we can calculate the number of ways to choose 4 journalists:

Number of ways = C(10, 4)

Let's calculate this:

Number of ways = 10! / (4!(10-4)!)

Number of ways = (10! / (4! * 6!))

Number of ways = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (6 * 5 * 4 * 3 * 2 * 1))

Number of ways = 210

Therefore, there are 210 ways to choose 4 journalists from a group of 10 for the thematic pages.

I hope this helps! Let me know if you have any further questions.