Question

Сколько различных трехзначных чисел можно составить из пяти цифр 1,2,3,4,5?

Answer 1

Считаем комбинаторными методами. Из пяти цифр можно выбрать три (5!/2!) количеством способов. Это 3х4х5 = 60. Но из этих чисел нужно изъять начинающиеся с нуля. Это - выбор двух цифр из четырёх, то есть (4!/2!) = 3х4 = 12. Итого получаем 60 - 12 = 48 чисел.

Answer 2

123 145 151 534 321 512

Answer 3

Calculating the Number of Different Three-Digit Numbers

To calculate the number of different three-digit numbers that can be formed from the digits 1, 2, 3, 4, and 5, we can use the formula for permutations of n objects taken r at a time, which is given by:

nPr = n! / (n - r)!

Where n is the total number of objects and r is the number of objects taken at a time.

Applying the Formula

In this case, we have 5 digits (1, 2, 3, 4, 5) and we want to form three-digit numbers. Therefore, we can calculate the number of different three-digit numbers using the formula:

5P3 = 5! / (5 - 3)!

Calculation

Using the formula, we can calculate the number of different three-digit numbers:

5! = 5 x 4 x 3 = 60

5P3 = 60 / 2 = 30

So, there are 30 different three-digit numbers that can be formed from the digits 1, 2, 3, 4, and 5.

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