Question

1)у круглого стола поставили 4 стула сколькими способами можно посадить на эти стулья А) 4 Детей б)3 детей в)2 детей 2)мальчика и двух девочек надо посадить за круглым столом с 4 стульями так чтобы девочки не оказались рядом сколькими способами это можно решить

Answer 1

1. а)4 детей смогут занять 4 стула 16 способамит потому что каждый ребенок может сесть на 4 стула б) 12 раз в) 8 раз
2.4 раза

Answer 2

1) У круглого стола поставили 4 стула. Сколькими способами можно посадить на эти стулья:

a) 4 детей? b) 3 детей? c) 2 детей?

To solve this problem, we can use the concept of permutations, as the order in which the children are seated matters.

a) If there are 4 children to be seated on the 4 chairs, we can calculate the number of ways using the formula for permutations of n objects taken all at a time, which is n!.

Therefore, the number of ways to seat 4 children on 4 chairs is 4! = 4 x 3 x 2 x 1 = 24 ways. b) If there are 3 children to be seated on the 4 chairs, we can calculate the number of ways using the same formula.

Therefore, the number of ways to seat 3 children on 4 chairs is 4P3 = 4 x 3 x 2 = 24 ways. c) If there are 2 children to be seated on the 4 chairs, we can calculate the number of ways using the same formula.

Therefore, the number of ways to seat 2 children on 4 chairs is 4P2 = 4 x 3 = 12 ways.

2) Мальчика и двух девочек надо посадить за круглым столом с 4 стульями так, чтобы девочки не оказались рядом. Сколькими способами это можно решить?

To solve this problem, we can use the concept of permutations with restrictions.

Let's consider the seating arrangement as follows: M represents the boy, G1 and G2 represent the two girls.

To ensure that the girls are not seated next to each other, we can consider two cases:

Case 1: The girls are seated on opposite sides of the boy. In this case, we can arrange the seating as follows: M G1 _ G2, where _ represents an empty chair.

The number of ways to arrange the seating in this case is 2! (since G1 and G2 can be interchanged) multiplied by 2! (since the remaining two chairs can be occupied by the boy and the empty chair in any order).

Therefore, the number of ways to arrange the seating in Case 1 is 2! x 2! = 4 ways.

Case 2: The girls are seated on the same side of the boy. In this case, we can arrange the seating as follows: G1 M G2 _ or G2 M G1 _.

The number of ways to arrange the seating in this case is 2! (since G1 and G2 can be interchanged) multiplied by 2 (since the remaining two chairs can be occupied by the boy and the empty chair in any order).

Therefore, the number of ways to arrange the seating in Case 2 is 2! x 2 = 4 ways.

To find the total number of ways to arrange the seating, we add the number of ways from Case 1 and Case 2.

Therefore, the total number of ways to arrange the seating is 4 + 4 = 8 ways.

Please note that the above solution assumes that the chairs are distinct and the children are distinct. If the chairs or children are identical, the number of ways may vary.