How many 4-digit even numbers can be created?

Question

I know that in unit place we can have 5 cases (0, 2, 4, 6, 8). In the leading position (thousandth place), should zero be allowed?

• 10 x 10 x 10 x 5
• 9 x 10 x 10 x 5 (This is what I believe should be the answer)

If either of these options are available, then we can choose any one. But what if both of these exists in the exam, then which one is correct?

Comments

Some answers to such question depends on context. If it was related to ATM pins, they can have leading zeroes, therefore in this case 10 x 10 x 10 x 5 is the correct answer. However in this question, it is mentioned "4 digit number", then we have different information, that it is a number and a 4 digit number can't start with 0, because we ignore the leading zeroes in numbers.

Answer 1

9x10x10x5  will be the answer , we have to ensure it is 4 digit number .

For such questions -

First fill critical  positions e.g. Here we have  L.S.B.  as critical position to ensure it is even number  , first fill it with (0,2,4,6,8) => 5 choices

Now second critical position is M.S.B.  to ensure it is 4 digit number , fill it with (1,2,...,9)    => 9 choices 

Now other positions can have any value from ( 0 to 9)   => 10 choices

 

Comments

Oh yes, I mixed up the concepts. Yes this is correct.