Question

Сколько различных трехзначных чисел можно составить с помощью цифр 7 2 0 3 цифры в записи числа не могут повторяться??!

Answer 1

18
7203 7230 7023 7032 7320 7302
2073 2037 2307 2037 2703 2730
3072 3023 3270 3207 3702 3720

Answer 2

Number of Different Three-Digit Numbers

To find the number of different three-digit numbers that can be formed using the digits 7, 2, 0, and 3 without repetition, we can use the concept of permutations.

Permutation Formula: The number of permutations of n distinct objects taken r at a time is given by the formula: \[ P(n, r) = \frac{n!}{(n-r)!} \]

Where: - n is the total number of objects - r is the number of objects taken at a time - ! denotes factorial

Calculation

Using the permutation formula, we can calculate the number of different three-digit numbers that can be formed using the given digits.

Step 1: Identify the values of n and r. - n = 4 (total number of digits: 7, 2, 0, 3) - r = 3 (three-digit numbers)

Step 2: Calculate the number of permutations. \[ P(4, 3) = \frac{4!}{(4-3)!} \]

\[ P(4, 3) = \frac{4!}{1!} \]

\[ P(4, 3) = 4 \times 3 \times 2 \]

Step 3: Solve for the number of permutations. \[ P(4, 3) = 24 \]

Therefore, 24 different three-digit numbers can be formed using the digits 7, 2, 0, and 3 without repetition.

(#1)