The number of different seven-digit numbers that can be written using only the three digit 1 , 2 and 3 with the condition that the digit 2 occurs twice in each number is7C2257p2257C252None of these

The problem is asking for the number of different seven-digit numbers that can be written using only the digits 1, 2, and 3, with the condition that the digit 2 must occur exactly twice in each number.

Here's how to solve it:

1. We have 7 positions to fill with the digits 1, 2, and 3.

2. Since the digit 2 must occur exactly twice, we choose 2 positions out of 7 for the digit 2. This can be done in 7C2 ways.

3. The remaining 5 positions can be filled with either 1 or 3. Since there are 2 choices for each position, this can be done in 2^5 ways.

4. Therefore, the total number of different seven-digit numbers is 7C2 * 2^5.

So, the answer is 7C2 * 2^5.