How many 4-digit numbers can be formed by using the digits 1 to 9 if repetition of digits is not allowed?
Answer: 3024
Step-by-step solution
Step 1: Identify the problem type
This problem asks for the number of ways to arrange a specific number of items (digits) from a larger set, where the order of arrangement matters and repetition is not allowed. This is a classic permutation problem.
Step 2: Determine available digits and number of places
We are given digits from 1 to 9, which means there are 9 distinct digits available. We need to form a 4-digit number, so there are 4 places to fill.
Step 3: Calculate choices for each position
For the first digit, we have 9 choices (any digit from 1 to 9). Since repetition is not allowed, for the second digit, we have 8 remaining choices. Similarly, for the third digit, we have 7 choices, and for the fourth digit, we have 6 choices.
Step 4: Apply the multiplication principle
According to the multiplication principle, the total number of ways to form the 4-digit number is the product of the number of choices for each position.
Step 5: Calculate the final result
Multiplying the number of choices for each position gives us the total number of unique 4-digit numbers that can be formed.
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