The number of 5 digit numbers that can be made using the digits 1 and 2 and in which at least one digit is different, is

Options

A. 30
B. 31
C. 32
D. none of these

Answer

To solve the problem of finding the number of 5-digit numbers that can be formed using the digits 1 and 2, where at least one digit is different, we can follow these steps:

### Step 1: Calculate the total number of 5-digit combinations
Each digit in a 5-digit number can either be a 1 or a 2. Therefore, for each of the 5 positions, we have 2 choices (1 or 2).

The total number of 5-digit combinations can be calculated as:
\[ \text{Total combinations} = 2^5 = 32 \]

### Step 2: Identify the invalid combinations
Out of the total combinations, we need to exclude the cases where all digits are the same. There are only two such cases:
1. 11111
2. 22222

### Step 3: Subtract the invalid combinations from the total
Now, we subtract the 2 invalid combinations from the total number of combinations:
\[ \text{Valid combinations} = 32 - 2 = 30 \]

### Conclusion
Thus, the number of 5-digit numbers that can be made using the digits 1 and 2, in which at least one digit is different, is:
\[ \boxed{30} \]

---