Question

The number of 5- digit numbers that can be made by using the digits 1 and 2 in which at least one digit is different, is
A. 30
B. 31
C. 32
D. none of these

Answer 1

Hint: We have to find the total numbers that can be made out of two digits 1 and 2 in which at least one digit is different. We can find this by simply finding out the total numbers that can be made from 1 and 2 and then subtracting those numbers which have digits 1 and 2 not different.

Complete step by step answer:
Now from the question we have,
We have to form a 5 digit number that can be made by 1and 2 there should be at least one digit different.
Now, for each of the place in 5- digit number we have 2 choices, hence the total number of 5- digit numbers are $2 \times 2 \times 2 \times 2 \times 2 = {2^5}$, out of these 32 number there are exactly two numbers namely 11111and 22222 that don’t satisfy the given condition.
Hence the total number of 5 digit numbers that can be made by using the digits 1 and 2 in which at least one digit is different is 32 – 2 = 30

So, option A is the correct answer.
Note:
For such types of questions that is basically from permutation and combination. Before starting we have to keep in mind that how many possible combinations are possible and based on the situation given in the question segregate the part like in the above question we can see that there are total 32 numbers that can made 5 digit numbers but there is a condition that in that 5digit numbers there should be at least one digit is different but when we see the possible combinations there are two such numbers that don’t follow the condition so we reduce that two numbers from our total numbers of combinations possible.