How many motor vehicle registration number plates can be formed with the digits 1, 2, 3, 4, 5 (No digits being repeated) if it is given that registration number can have 1 to 5 digits?

Options

A. 100
B. 120
C. 325
D. 205

Answer

To solve the problem of how many motor vehicle registration number plates can be formed with the digits 1, 2, 3, 4, 5 (with no digits being repeated) and where the registration number can have 1 to 5 digits, we will calculate the possibilities for each case (1-digit, 2-digit, 3-digit, 4-digit, and 5-digit numbers) and then sum them up.

### Step-by-Step Solution:

1. **1-Digit Numbers:**
- We can use any of the 5 digits (1, 2, 3, 4, 5).
- Total possibilities = 5.

2. **2-Digit Numbers:**
- For the first digit, we have 5 options (1, 2, 3, 4, 5).
- After choosing the first digit, we have 4 options left for the second digit.
- Total possibilities = 5 × 4 = 20.

3. **3-Digit Numbers:**
- For the first digit, we have 5 options.
- For the second digit, we have 4 options (after choosing the first).
- For the third digit, we have 3 options (after choosing the first two).
- Total possibilities = 5 × 4 × 3 = 60.

4. **4-Digit Numbers:**
- For the first digit, we have 5 options.
- For the second digit, we have 4 options.
- For the third digit, we have 3 options.
- For the fourth digit, we have 2 options.
- Total possibilities = 5 × 4 × 3 × 2 = 120.

5. **5-Digit Numbers:**
- For the first digit, we have 5 options.
- For the second digit, we have 4 options.
- For the third digit, we have 3 options.
- For the fourth digit, we have 2 options.
- For the fifth digit, we have 1 option.
- Total possibilities = 5 × 4 × 3 × 2 × 1 = 120.

6. **Total Registration Numbers:**
- Now, we sum all the possibilities from each case:
- Total = 5 (1-digit) + 20 (2-digit) + 60 (3-digit) + 120 (4-digit) + 120 (5-digit)
- Total = 5 + 20 + 60 + 120 + 120 = 325.

### Final Answer:
The total number of motor vehicle registration number plates that can be formed is **325**.