Final answer:
To find the number of odd numbers with a middle digit of 5 between 40000 and 69999 with no repeated digits, multiply the number of choices for each digit.
Step-by-step explanation:
To find the number of odd numbers with a middle digit of 5 between 40000 and 69999 with no repeated digits, we can break down the problem into steps:
Choose the first digit. Since the numbers must be between 40000 and 69999, the first digit can be either 4, 5, or 6. This gives us 3 choices for the first digit.
Choose the last digit. Since we are looking for odd numbers, the last digit must be 1, 3, 5, 7, or 9. This gives us 5 choices for the last digit.
Choose the remaining two digits. Since no digits can be repeated, we have 8 choices for the second digit (excluding the already chosen first and last digits), and 7 choices for the third digit (excluding the first, second, and last digits).
By multiplying the choices together, we get 3 * 5 * 8 * 7 = 840 possible odd numbers with a middle digit of 5 between 40000 and 69999 with no repeated digits.