Question

Сколько существует перестановок букв слова конус в которых буквы к,о,н стоят рядом в указанном порядке

Answer 1

конус, консу, уконс, скону, ускон, сукон

Ответ: 6

Answer 2

Calculation of Permutations

To calculate the number of permutations of the word "конус" where the letters "к", "о", and "н" are adjacent in the specified order, we can use the concept of permutations with restrictions.

The word "конус" has 5 letters. We want to find the number of permutations where the letters "к", "о", and "н" are adjacent in the order "кон".

To solve this, we can treat the group of three letters "кон" as a single entity. So, we have 3 entities: "кон", "у", and "с".

The number of permutations of these 3 entities is given by the formula: n! / (n1! * n2! * ... * nk!), where n is the total number of entities and n1, n2, ..., nk are the number of repetitions of each entity.

In this case, we have 3 entities: "кон" (1 repetition), "у" (1 repetition), and "с" (1 repetition). Therefore, the number of permutations is:

5! / (1! * 1! * 1!) = 5! / 1 = 5 * 4 * 3 * 2 * 1 / 1 = 120

So, there are 120 permutations of the word "конус" where the letters "к", "о", and "н" are adjacent in the specified order.