Question

Сколько различных восьмизначных чисел можно получить, используя в их написании цифру 1 два раза, а цифры 2 и 3 – по три раза?

Answer 1

Ответ:

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Answer 2

Calculating the Number of Eight-Digit Numbers

To calculate the number of different eight-digit numbers that can be formed using the digit 1 twice, and the digits 2 and 3 three times, we can use the concept of permutations.

The total number of ways to arrange the digits is given by the formula for permutations of a multiset, which is:

Total number of arrangements = 8! / (2! * 3! * 3!)

Where: - 8! represents the factorial of 8 (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) - 2! represents the factorial of 2 (2 * 1) for the repeated digit 1 - 3! represents the factorial of 3 (3 * 2 * 1) for the repeated digit 2 - 3! represents the factorial of 3 (3 * 2 * 1) for the repeated digit 3

Calculation

Using the formula, we can calculate the total number of arrangements:

Total number of arrangements = 8! / (2! * 3! * 3!)

Total number of arrangements = (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (2 * 1 * 3 * 2 * 1 * 3 * 2 * 1)

Total number of arrangements = 40,320 / (2 * 6 * 6)

Total number of arrangements = 40,320 / 72

Total number of arrangements = 560

So, there are 560 different eight-digit numbers that can be formed using the digit 1 twice, and the digits 2 and 3 three times.

This calculation is based on the concept of permutations and the specific arrangement of the given digits.