Question

Сколько трёхзначных чисел с различными цифрами можно составить из цифр 0,2,4,7,8,9?

Answer 1

100 трёхзначных чисел 

Answer 2

Answer in detail. How many three-digit numbers with different digits can be formed from the digits 0,2,4,7,8,9?

To answer this question, we need to consider two cases: when the first digit is zero and when it is not.

- If the first digit is zero, then we have only one choice for it. Then, we have five choices for the second digit (2,4,7,8,9) and four choices for the third digit (any of the remaining digits). Therefore, the number of three-digit numbers with different digits that start with zero is 1 x 5 x 4 = 20. - If the first digit is not zero, then we have five choices for it (2,4,7,8,9). Then, we have five choices for the second digit (any of the other digits, including zero) and four choices for the third digit (any of the remaining digits). Therefore, the number of three-digit numbers with different digits that do not start with zero is 5 x 5 x 4 = 100.

Adding these two cases, we get the total number of three-digit numbers with different digits that can be formed from the digits 0,2,4,7,8,9 as 20 + 100 = 120.