The number of 7-digit numbers the sum of whose digits is even is

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10^{5}

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10^{5}

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10^{5}

None of these

answer is B.

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Detailed Solution

Concept- The total number of 7-digit numbers that can exist must be determined. Permutations of the numbers that can be in each digit place can be used to find this. The entire number of 7-digit numbers is even divided by the numbers with the sum of the digits.
There are seven locations in a seven-digit number. Numbers from 0 to 9 may be used in each of the seven locations aside from the first digit. The numbers other than 0 can be used in the place of the first digit, though. Therefore, we can utilize digits 1 through 9. This is because the number won't be seven digits if there is a zero there. It will change into a number with six digits or fewer. Therefore, by multiplying the number of possible numbers at each digit's place, one can get the number of seven-digit numbers that are feasible.
This gives us the total amount of seven-digit numbers. =

Half of all 7-digit numbers have the sum of the digits be an odd number, which is rare.
As a result, there are 7-digit numbers with an even sum of digits.

Hence, the correct option is