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The problem asks to find the number of possible three-digit numbers that can be formed using the digits of the number 20250131.

Discrete MathematicsCountingCombinatoricsPermutationsDigit Manipulation
2025/6/14

1. Problem Description

The problem asks to find the number of possible three-digit numbers that can be formed using the digits of the number
2
0
2
5
0
1
3
1.

2. Solution Steps

The digits of the number 20250131 are 0, 1, 2, 3, and

5. We need to form a three-digit number using these digits.

The digits can be repeated. However, the first digit of a three-digit number cannot be
0.
The available digits are:
0 (appears twice)
1 (appears twice)
2 (appears once)
3 (appears once)
5 (appears once)
To form a three-digit number, we have three places to fill: _ _ _
The first digit can be any digit except

0. So, we have 4 choices (1, 2, 3, 5).

The second digit can be any of the digits (0, 1, 2, 3, 5). So, we have 6 choices if the digits can be repeated.
The third digit can also be any of the digits (0, 1, 2, 3, 5). So, we have 6 choices if the digits can be repeated.
Therefore, the total number of three-digit numbers is 5×6×6=1805 \times 6 \times 6 = 180.
However, we only have the digits 0, 1, 2, 3,

5. So the number of total choices is actually 5 since there are 5 available digits.

Let us first find the number of distinct three-digit numbers when we can use the digits multiple times: 0, 1, 2, 3,

5. For the first digit, we can use 1, 2, 3,

5. So we have 4 choices.

For the second digit, we can use 0, 1, 2, 3,

5. So we have 5 choices.

For the third digit, we can use 0, 1, 2, 3,

5. So we have 5 choices.

Therefore, the number of three-digit numbers is 4×5×5=1004 \times 5 \times 5 = 100.
Consider the possible options given:
A. 400
B. 600
C. 06
D. 74
E. 62

3. Final Answer

Since the answer 100 is not among the options, and we are dealing with digits of a specific number (20250131), and some of the digits are repeated, it is likely that the task is to consider only some of the digits of the given number. The available digits are 0, 1, 2, 3, 5, with multiplicities 2, 2, 1, 1,

1. The only provided possible solutions are single or double digits. This suggests that the question is mistranslated and there is no way of solving it with this information. The closest to the result above is "74".

Final Answer: D. 74

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