Question

3. Пещерный человек Ы собирается последовательно подружиться с четырьмя соседями: Ау, Оу, Уу и Ыу. Каким числом способов он может это сделать, если с Ыу можно подружиться только после Оу?

Answer 1

общее количество вариантов без Ыу равно 6, расмотрим их подробнее

АОУ - может быть расширен до двух АОУЫ и АОЫУ (2)

АУО - может преобразоваться только в АУОЫ (1)

ОАУ - может быть расширен до трех ОАУЫ ОАЫУ ОЫАУ (3)

ОУА - три ОУАЫ ОУЫА ОЫУА(3)

УАО - один УАОЫ(1)

УОА - два УОАЫ УОЫА(2)

итого общее кол-во вариантов 2+1+3+3+1+2 = 12

Ответ 12

 

 

Answer 2

Number of Ways to Befriend Neighbors

The cave person, let's call them "Y", wants to befriend their four neighbors: "A", "O", "U", and "YU". However, Y can only befriend "YU" after befriending "O". We need to determine the number of ways Y can accomplish this.

To solve this problem, we can use a simple counting technique. Since Y can only befriend "YU" after befriending "O", we can treat "O" and "YU" as a single entity. This means we have three entities to arrange: "A", "U", and the combined entity "OYU".

The number of ways to arrange these three entities can be calculated using the factorial function. The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n.

In this case, we have three entities, so the number of ways to arrange them is 3!.

3! = 3 x 2 x 1 = 6

Therefore, there are 6 ways for Y to befriend their neighbors, given the condition that YU can only be befriended after O.

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