Answer:
To find out how many three-digit numbers can be formed from the digits 1, 2, 6, 3, and 5 (without repetition), we can use the concept of permutations.
Since we are forming three-digit numbers, we need to consider the following:
1. The first digit cannot be 0.
2. The digits must be distinct (without repetition).
The number of ways to arrange n distinct objects is given by n! (n factorial).
For this problem:
- We have 5 digits to choose from for the first digit.
- Once the first digit is chosen, we have 4 remaining digits for the second digit.
- After selecting the first two digits, we have 3 remaining digits for the third digit.
Therefore, the total number of three-digit numbers that can be formed is:
5 (choices for the first digit) * 4 (choices for the second digit) * 3 (choices for the third digit) = 60
Hence, there are 60 three-digit numbers that can be formed from the digits 1, 2, 6, 3, and 5 without repetition.
