The question is asking how many two-digit odd numbers can be formed using the digits $1, 2, 3, 4, 5$, with repetition allowed.

Steps to Solve:

1. First digit (tens place):

   • The number is two digits long, so the first digit can be any of the five digits: $1, 2, 3, 4, 5$.
   • Thus, there are 5 possible choices for the first digit.

2. Second digit (ones place):

   • Since the number needs to be odd, the second digit (the ones place) must be an odd digit.
   • The odd digits from the given set are $1, 3, 5$.
   • Therefore, there are 3 possible choices for the second digit.

3. Total number of two-digit odd numbers:

   • Since repetition is allowed, the total number of such numbers is given by: $5 \times 3 = 15$

Thus, the correct answer is B) 15.

Would you like more details or have any other questions?

Here are five related questions to expand your understanding:

1. How would the answer change if repetition was not allowed?
2. What if only even numbers were allowed instead of odd numbers?
3. How many two-digit numbers can be formed if repetition is not allowed, and the number must be even?
4. What if the number of digits was increased to three? How would the calculations change?
5. How would the total change if the available digits included 0?

Tip: When solving these kinds of counting problems, focus on restrictions (like odd/even digits) to narrow down your choices for each digit.