Question

The total number of seven – digit numbers the sum of whose digits is even is
A.9000000
B.4500000
C.8100000
D.None of these

Answer 1

Hint: In this question, we need seven - digits numbers the sum of whose digits is even. It means we have 0, 2, 4, 6, 8 at the unit place. Let’s understand this with these boxes below:

Complete step-by-step answer:
We know that even numbers have 0 ,2, 4, 6, 8 at unit place.
To form seven – digit numbers
At 1st place we could have 9 digits to fill from 1 to 9. We have excluded 0 because zero can’t be put at first place.
At the 2nd place we can fill 10 digits from 0 to 9.
At 3rd place we can fill 10 digits from 0 to 9.
At the 4th place we can fill 10 digits from 0 to 9.
Similarly, at 5th and 6th place we can fill 10 digits from 0 to 9.
At the last or unit place we have 5 digits to fill that is 0, 2, 4, 6, 8.
Hence, the total number of seven – digit numbers the sum of whose digits is even is
 = 9 × 10 × 10 × 10 × 10 × 10 × 5
 = 4500000 (Ans.)

Note: In this question, you have noticed that we have not put zero at the first place because if we have placed 0 then it would become a six – digit number. That is why in the first place we have 9 ways to fill the box. But in the next five places we can have 10 ways for each. And at last place or unit place we have only even numbers 0, 2, 4, 6, 8 (5 ways).