Answer

Verified

402.3k+ views

**Hint:**

Firstly, we need to find the total number of 7-digit numbers. This we can find by calculating the number of permutations at each digit’s place. The numbers with sum of digits as even will be the half of total 7-digit numbers.

**Complete step by step solution:**

We know that there are 7 digit places in a 7-digit number. In each place except the ${1}^{\text{st}}$ digit place, numbers from 0 to 9 can be used. For a number to be a 7-digit number at the ${1}^{\text{st}}$ digit place numbers from 1 to 9 can be used (because using 0 at ${1}^{\text{st}}$ digit place will make the number a 6-digit or lesser number). So, we can obtain the number of all possible seven digit numbers by multiplying all possible numbers at each digit’s place.

Thus, the all possible 7-digit numbers is given by

$

9 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \\

\Rightarrow 9 \times {10^6} \\

$

Now, half of these numbers have the sum of their digits as an odd number. So, the other half of these numbers have their sum of digits as an even number.

$

\dfrac{1}{2} \times 9 \times {10^6} \\

\Rightarrow 45 \times {10^5} \\

$

**Therefore, the correct answer is B.**

**Note:**

The concept of half of numbers as an even number or an odd number is valid for any number of digits. We can use permutations to calculate the total numbers for any number of digits. Permutation is always used to get the arrangement of items.

Recently Updated Pages

Define the following A 1 volt PD B Electric power class 12 physics CBSE

In a halfwave rectifier the rms value of the ac component class 12 physics CBSE

When light travels from a rarer to a denser medium class 12 physics CBSE

The unit of electric dipole moment is A Newton B Coulomb class 12 physics CBSE

The waveforms A and B given below are given as input class 12 physics CBSE

What is the cause of Presbyopia class 12 physics CBSE

Trending doubts

Difference Between Plant Cell and Animal Cell

Mention the different categories of ministers in the class 10 social science CBSE

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Who is the executive head of the Municipal Corporation class 6 social science CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Which monarch called himself as the second Alexander class 10 social science CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE

Write an application to the principal requesting five class 10 english CBSE