Question

Ваня знает что номер телефона его друга состоит из четырех цифр 1,2,3,4,но не помнит,в каком порядке их надо набирать.Сколько вариантов в худшем случае ему придется перебрать,чтобы дозвониться до друга?

Answer 1

Пусть первая цифра 1, тогда вариантов шесть:

1 2 3 4

1 2 4 3

1 3 2 4

1 3 4 2

1 4 2 3 

1 4 3 2

И так будет с каждой цифрой, то есть всего вариантов 4*6 = 24.

Если Вы знаете, что такое факториал, то количество перестановок n элементов равно n!

В данной задаче число вариантов 4! = 1*2*3*4 = 24.

Answer 2

The Question

Vanya knows that his friend's phone number consists of the digits 1, 2, 3, 4, but he does not remember the order in which to dial them. How many variants would he have to try at worst to call his friend?

The key facts are: - Vanya's friend's phone number consists of the digits 1, 2, 3, 4 - Vanya does not remember the order of the digits - We need to determine the maximum number of variants Vanya would have to try at worst to call his friend

Determining the Number of Variants

Since there are 4 digits that can be arranged in any order, and each digit position can be filled by any of the 4 digits, this is a classic permutation problem.

The number of permutations of n unique objects taken r at a time (order matters) is given by:

`P(n, r) = n! / (n - r)!`

Where `n!` is `n` factorial.

In this case: - `n` = 4 (number of available digits) - `r` = 4 (number of digit positions to fill)

Plugging into the formula: `P(4, 4) = 4! / (4 - 4)! = 4 * 3 * 2 * 1 = 24`

Therefore, the maximum number of variants Vanya would have to try is 24.