Question

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

• A. 31
• B. 32
• C. 30
• D. 29

Answer 1

The correct option is C 30

We will find the total number of 5-digit numbers that can be formed using the digits $2$ and $1$ only and remove the number which has all the digits same.
Now, for each of the place in 5-digit number we have $2$ choices, hence the total number of 5-digit numbers are $2^5$. out of these 32 number there are exactly two number namely $11111$ and $22222$ do not satisfy the given condition. Hence the total 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 $32-2=30$