Question

!!! Сколько пятизначных телефонных номеров можно составить используя цифры 3, 4, 5, 6, 7 (без повторений)?​

Answer 1

Ответ: 120

Объяснение:

Используем формулу для перестановок из 5 элементов

Р5=5!=120

Answer 2

Calculating the Number of Five-Digit Phone Numbers

To calculate the number of five-digit phone numbers that can be formed using the digits 3, 4, 5, 6, and 7 without repetitions, we can use the concept of permutations.

The number of ways to arrange n distinct items is given by n!, where "!" denotes the factorial of a number. The factorial of a number is the product of all positive integers less than or equal to that number.

The formula for calculating the number of permutations of n items taken r at a time is given by nPr = n! / (n - r)!. In this case, we want to find the number of permutations of 5 items taken 5 at a time using the digits 3, 4, 5, 6, and 7.

Calculation

Using the formula nPr = n! / (n - r)!, where n = 5 and r = 5: - The number of permutations of 5 items taken 5 at a time is 5! / (5 - 5)! - This simplifies to 5! / 0!, and since 0! = 1, the expression becomes 5! / 1 - Therefore, the number of permutations is 5! = 5 x 4 x 3 x 2 x 1 = 120

So, the number of five-digit phone numbers that can be formed using the digits 3, 4, 5, 6, and 7 without repetitions is 120.