Repeatition not allowed

How many four-digit numbers can be formed from the digits 3, 5, 8, and 9 if no digit may be repeated?

Final Answer:

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Dr. Math

To determine how many four-digit numbers can be formed from the digits 3, 5, 8, 9 without repeating any digit, we can use the permutation concept. Since the order of digits matters in forming a number, we'll calculate the number of possible arrangements (permutations) of these four digits.

Step-by-Step Solution:

1. First Digit (Thousands place):
- You have 4 choices (3, 5, 8, 9).

2. Second Digit (Hundreds place):
- After choosing the first digit, 3 digits remain.
- So, you have 3 choices.

3. Third Digit (Tens place):
- After choosing the first two digits, 2 digits remain.
- So, you have 2 choices.

4. Fourth Digit (Ones place):
- After choosing the first three digits, only 1 digit remains.
- So, you have 1 choice.

Calculating the Total Number of Four-Digit Numbers:

Multiply the number of choices for each digit position:

4 (choices for first digit) × 3 (choices for second digit) × 2 (choices for third digit) × 1 (choice for fourth digit) = 4 × 3 × 2 × 1 = 24

Final Answer: