I held an objection to this question. Here it is mentioned that the first two numbers will be the last two digits of the birth year and followed by five other numerical digits. Therefore, the other five digits should not be different from the last two digits of the birth year?

There is no specification or instruction in the question.

The only constraint is the first two. The others can be from zero to nine as a unit digits


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I am a bit confused regarding the solution to this problem. The common solution procedure is as follows:

It is a 7-digit number.
The choice for the first digit is only 1 i.e. 8.
The choice for second digit is 3 i.e. 0, 1 and 2.

Since the question hasn't put any specific restrictions, the choice for the third digit is 10 i.e. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
And for the fourth, fifth, sixth, and seventh digits, the choices as still 10, since the example in the question indicates that repetition is possible.

Now total number of possible outcomes is:
1*3*10*10*10*10*10 = 300000.

Now here is my doubt: when we get the answer by multiplying all these choices, doesn't it mean that shuffling is possible? The question specifically indicates that the first two digits must only be 80, 81 and 82. And their position can't change. I doubt that with this multiplication, shuffling between numbers is allowed. Can anyone kindly clarify?

The Answer is D
1980-82 that means 3 years: 1980, 1981, 1982.
Also the number of such identification numbres for each year will remain the same. Thus we will calculate the number for 1 year and then multiply it by 3.

For the year 1980
We have 07 slots: __ __ __ __ __ __ __
Out of which the first 2 are fixed: 8 0 __ __ __ __ __
Now, since the numbers can be repeated, we can fill each of the remaining 05 slots in 10 ways(0-9) each.
Hence the total Number of such IDs for 1980 is: 1x1x10x10x10x10x10 = 100000

Now since we need to do the same for 3 years
we can safely calculate the grand total: 3x100000
=3,00,000