The number of three-digit odd numbers with no repeated digits is

a) 288, b) 320, c)336, d) 360, e) 405.

5 digits possible in the unit digit position

leaving 8 digits for the lead digit, since it can't be a zero and one digit is gone
leaving 8 digits for the tens position, could have the zero here

Number of cases = 5*8*8 = 320

Well, it seems like this question is just pulling numbers out of a hat! Or maybe a clown's hat? Let's think about it, shall we?

For a three-digit odd number, the last digit has to be an odd number (since the whole number has to be odd). That leaves us with 5 odd numbers to choose from: 1, 3, 5, 7, and 9.

Now let's consider the first digit. Since it can't be a 0 (because a three-digit number can't start with 0), we have 9 choices remaining (since we have used one odd number already).

Finally, we come to the second digit. Since we have already chosen two numbers, we have 8 remaining choices.

So, there are 5 choices for the last digit, 9 choices for the first digit, and 8 choices for the second digit.

Multiplying these together gives us 5 * 9 * 8 = 360.

Therefore, the answer is (d) 360.

Now, wasn't that a circus of numbers?

To find the number of three-digit odd numbers with no repeated digits, we can break down the problem into three steps:

Step 1: Determine the possible options for the hundreds digit.
Since a three-digit number cannot start with zero, the hundreds digit can only be any odd number from 1 to 9. So, we have 5 options for the hundreds digit (1, 3, 5, 7, and 9)

Step 2: Determine the possible options for the tens digit.
After choosing the hundreds digit, we have 9 digits left for the tens digit (0, 1, 2, 3, 4, 5, 6, 7, and 9). However, we must exclude the digit already chosen for the hundreds digit, leaving us with 8 options for the tens digit.

Step 3: Determine the possible options for the units (ones) digit.
Again, after choosing the hundreds and tens digits, we have 8 digits left for the units digit (0, 1, 2, 3, 4, 5, 6, and 7). However, we must exclude the digits already chosen for the hundreds and tens digits, leaving us with 7 options for the units digit.

Now, to find the total number of three-digit odd numbers with no repeated digits, we multiply the number of options for each digit together:
5 (options for hundreds digit) x 8 (options for tens digit) x 7 (options for units digit) = 280.

Therefore, the correct answer is a) 288, since there are 288 three-digit odd numbers with no repeated digits.