Question

Сколько имеется 8-значных чисел, в которых имеется хотя бы две одинаковые цифры?

Answer 1

Всего поидее восьмизначных чисел 90000000. Из них со всеми разными цифрами 9*9*8*7*6*5*4*3.(Первая цифра любая из 1-9,вторая любая из 0-9,кроме той,что выбрали уже,третья любая из 0-9 кроме двух выбранных и т.д.).Из 9*10^8 вычитаем  это большое произведение,получаем 88367040 чисел. 

Answer 2

Count of 8-Digit Numbers with at Least Two Identical Digits

To calculate the count of 8-digit numbers with at least two identical digits, we can consider the total count of 8-digit numbers and then subtract the count of 8-digit numbers with all unique digits.

Total Count of 8-Digit Numbers: The total count of 8-digit numbers can be calculated using the formula: 9 * 10^7. This is because the first digit cannot be zero, so it has 9 possibilities (1-9), and the subsequent digits can be any of the 10 digits (0-9).

Count of 8-Digit Numbers with All Unique Digits: The count of 8-digit numbers with all unique digits can be calculated using the permutation formula: 10P8. This is because there are 10 digits available (0-9), and we need to choose 8 of them without repetition.

Calculation

Using the above information, we can calculate the count of 8-digit numbers with at least two identical digits as follows:

Total Count of 8-Digit Numbers = 9 * 10^7 Count of 8-Digit Numbers with All Unique Digits = 10P8

Now, we can calculate the count of 8-digit numbers with at least two identical digits by subtracting the count of 8-digit numbers with all unique digits from the total count of 8-digit numbers:

Count of 8-Digit Numbers with at Least Two Identical Digits = Total Count of 8-Digit Numbers - Count of 8-Digit Numbers with All Unique Digits

Let's calculate this:

Total Count of 8-Digit Numbers = 9 * 10^7 = 90,000,000 Count of 8-Digit Numbers with All Unique Digits = 10P8 = 10! / (10-8)! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 = 40,320

Count of 8-Digit Numbers with at Least Two Identical Digits = 90,000,000 - 40,320 = 89,959,680

Therefore, there are 89,959,680 8-digit numbers in which there are at least two identical digits.

I hope this helps! If you have further questions or need additional assistance, feel free to ask.