The question asks for the number of odd four-digit numbers less than 3,000 that can be formed using the digits {1, 2, 3, 4, 5} without repetition.

Step-by-step explanation:

1. Understanding the conditions:

   • We need to form a four-digit number.
   • The number must be odd, so the last digit must be one of {1, 3, 5}.
   • The number must be less than 3,000, so the first digit can only be 1 or 2.
   • Repetition of digits is not allowed.

2. Choosing the digits:

   • First digit: To ensure the number is less than 3,000, the first digit must be either 1 or 2. So, we have 2 options for the first digit.
   • Fourth digit (the last digit): Since the number must be odd, the last digit must be chosen from {1, 3, 5}. Therefore, there are 3 options for the last digit.
   • Second and third digits: After selecting the first and fourth digits, we cannot reuse those digits. This leaves 3 digits from the set {1, 2, 3, 4, 5} to choose for the second digit and 2 digits to choose for the third digit.

3. Counting the possibilities:

   • For the first digit: 2 options (1 or 2).
   • For the last digit: 3 options (1, 3, 5).
   • For the second digit: After choosing the first and last digits, 3 digits remain, so there are 3 options.
   • For the third digit: After choosing the first, second, and last digits, 2 digits remain, so there are 2 options.

4. Calculating the total number of numbers: $2 \text{ (choices for first digit)} \times 3 \text{ (choices for last digit)} \times 3 \text{ (choices for second digit)} \times 2 \text{ (choices for third digit)} = 36$

Thus, the total number of odd four-digit numbers less than 3,000 that can be formed is 36.

Would you like more details or further explanation? Here are some related questions:

1. How would the answer change if repetition of digits were allowed?
2. What would be the total number of even four-digit numbers less than 3,000 with the same conditions?
3. Can you form a three-digit odd number from the set {1, 2, 3, 4, 5}?
4. How many four-digit numbers less than 3,000 can be formed if no restriction is placed on the last digit being odd?
5. How does the counting principle apply in this type of permutation problem?

Tip: When dealing with permutations and combinations, always pay attention to any restrictions (like repetition or parity) and carefully break down your counting steps.