A number plate of a vehicle has always a fixed code UP-32 for Lucknow city followed by the number of particular vehicle which is in two parts. First part is occupied by 2 English alphabets and second part is occupied by 4 digit numbers(0001,0002, ....9999). If the latest registration number of vehicle is {UP-32
SK-0123}, find the number of vehicles registered before this vehicle number in Lucknow.

Options

A. A) 2449744
B. B) 4779644
C. B) 4669235
D. D) 9235888222

Answer

To find the total number of vehicles registered before the vehicle number UP-32 SK-0123 in Lucknow, we will break down the problem into manageable steps.

### Step-by-Step Solution:

1. **Identify the Fixed Code**:
The fixed code for all vehicles in Lucknow is UP-32.

2. **Determine the Format of the Registration Number**:
The registration number consists of two parts:
- The first part has 2 English alphabets (e.g., SK).
- The second part has a 4-digit number (e.g., 0123).

3. **Count the Combinations for the First Part (Two Alphabets)**:
- The first letter can be any letter from A to R (since S is the first letter of the latest registration SK).
- There are 18 letters from A to R (A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R).
- The second letter can be any letter from A to Z (26 letters).
- Thus, the total combinations for the first part before SK is:
\[ 18 \text{ (choices for the first letter)} \times 26 \text{ (choices for the second letter)} = 468 \]

4. **Count the Combinations for the Second Part (Four Digits)**:
- The four-digit numbers range from 0001 to 9999, giving us a total of 9999 combinations.
- Therefore, the total combinations for the first part (up to RZ) with all four-digit numbers is:
\[ 468 \times 9999 = 4,668,432 \]

5. **Count the Combinations for the First Letter 'S' and Second Letter 'K'**:
- For the first letter 'S', the second letter can be from A to J (10 letters).
- The total combinations for the second part (0001 to 9999) remains 9999.
- Thus, the total combinations for SK with all four-digit numbers up to SJ is:
\[ 1 \text{ (for S)} \times 10 \text{ (choices for the second letter A to J)} \times 9999 = 99,990 \]

6. **Count the Numbers Before 0123**:
- The numbers from 0001 to 0122 are 122 numbers.
- Therefore, we need to add these to our total.

7. **Calculate the Total Vehicles Registered Before SK-0123**:
- Now, we sum all the combinations:
\[ \text{Total} = 4,668,432 + 99,990 + 122 = 4,768,544 \]

### Final Answer:
The total number of vehicles registered before the vehicle number UP-32 SK-0123 in Lucknow is **4,768,544**.