Question

В списке учеников 6 класса 15 девочек и 13 мальчиков нужно выделить группы из трех человек для посещения заболевшего ученика этого класса сколькими способами это можно сделать1 и если все члены группы девочки2 все члены группы мальчики 3 в группе одна девочка и два мальчика g в группе две девочки один мальчик.

Answer 1

Заболел ученик,значит выбор между 15 девочками и 12 мальчиками
1)все члены группы девочки
Число сочетаний 3 из 15 равно
15!/(3!*12!)=12!*13*14*15/(12!*1*2*3)=455 способов
2)все члены группы мальчики
Число сочетаний 3 из 12 равно
12!/(3!*9!)=9!*10*11*12/(9!*1*2*3)=220 способов
3) в группе одна девочка и два мальчика
Произведение числа сочетаний 1 из 15 на число сочетаний 2 из 12 равно
15!/14! *12!/(2!*10!)=15*10!*11*12/(10!*1*2)=15*66=990 способов
4)в группе две девочки один мальчик
Произведение числа сочетаний 2 из 15 на число сочетаний 1 из 12 равно
15!/(13!*2!)*12=13!*14*15/(13!*1*2)*12=105*12=1260 способов

Answer 2

Calculation of the Number of Ways to Form Groups

To determine the number of ways to form groups of three students from a class of 15 girls and 13 boys, we can use combinations.

1. If we want to form groups where all members are girls, we can choose 3 girls from the 15 available. The number of ways to do this is given by the combination formula:

Number of ways = C(15, 3)

The combination formula is defined as:

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

where n is the total number of items, r is the number of items to be chosen, and ! denotes the factorial of a number.

2. If we want to form groups where all members are boys, we can choose 3 boys from the 13 available. The number of ways to do this is given by the combination formula:

Number of ways = C(13, 3)

3. If we want to form groups where one girl and two boys are in each group, we can choose 1 girl from the 15 available and 2 boys from the 13 available. The number of ways to do this is given by the product of the two combination formulas:

Number of ways = C(15, 1) * C(13, 2)

4. If we want to form groups where two girls and one boy are in each group, we can choose 2 girls from the 15 available and 1 boy from the 13 available. The number of ways to do this is given by the product of the two combination formulas:

Number of ways = C(15, 2) * C(13, 1)

Let's calculate the number of ways for each scenario.

Calculation:

1. Number of ways to form groups with all girls: - Number of ways = C(15, 3) = 455 2. Number of ways to form groups with all boys: - Number of ways = C(13, 3) = 286 3. Number of ways to form groups with one girl and two boys: - Number of ways = C(15, 1) * C(13, 2) = 15 * 78 = 1170 4. Number of ways to form groups with two girls and one boy: - Number of ways = C(15, 2) * C(13, 1) = 105 * 13 = 1365 Therefore, the number of ways to form groups of three students from the given class are as follows: 1. All girls: 455 ways 2. All boys: 286 ways 3. One girl and two boys: 1170 ways 4. Two girls and one boy: 1365 ways

Please let me know if there is anything else I can help you with!