Total number of four digit odd numbers that can be formed by using `0, 1, 2, 3, 5, 7` are

Options

A. 216
B. 375
C. 400
D. 720

Answer

To find the total number of four-digit odd numbers that can be formed using the digits `0, 1, 2, 3, 5, 7`, we need to follow these steps:

### Step 1: Identify the conditions for a four-digit number
A four-digit number cannot start with `0`. Additionally, since we want the number to be odd, the last digit must be an odd digit.

### Step 2: Identify the available digits
The available digits are `0, 1, 2, 3, 5, 7`. Among these, the odd digits are `1, 3, 5, 7`.

### Step 3: Choose the last digit (odd digit)
Since the four-digit number must be odd, we can choose the last digit from the odd digits. The available odd digits are `1, 3, 5, 7`, which gives us 4 choices for the last digit.

### Step 4: Choose the first digit
The first digit can be any of the digits except `0`. Therefore, the possible choices for the first digit are `1, 2, 3, 5, 7`, which gives us 5 choices.

### Step 5: Choose the second digit
The second digit can be any of the available digits, including `0`. Since we have `0, 1, 2, 3, 5, 7`, we have 6 choices for the second digit.

### Step 6: Choose the third digit
The third digit can also be any of the available digits, including `0`. Thus, we again have 6 choices for the third digit.

### Step 7: Calculate the total combinations
Now, we can calculate the total number of four-digit odd numbers using the formula:
\[ \text{Total combinations} = (\text{Choices for first digit}) \times (\text{Choices for second digit}) \times (\text{Choices for third digit}) \times (\text{Choices for last digit}) \]
Substituting the values we found:
\[ \text{Total combinations} = 5 \times 6 \times 6 \times 4 \]

### Step 8: Perform the calculation
Calculating the above expression:
\[ 5 \times 6 = 30 \]
\[ 30 \times 6 = 180 \]
\[ 180 \times 4 = 720 \]

Thus, the total number of four-digit odd numbers that can be formed is **720**.

### Final Answer
The total number of four-digit odd numbers that can be formed using the digits `0, 1, 2, 3, 5, 7` is **720**.

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