The total number of seven-digit numbers the s | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the seven-digit number be represented as $x_1x_2x_3x_4x_5x_6x_7$.The first digit $x_1$ can take any value from $1$ to $9$ ($9$ choices).The di

Vedclass · Accepted Answer

$4500000$

Vedclass · Answer

(B) Let the seven-digit number be represented as $x_1x_2x_3x_4x_5x_6x_7$.The first digit $x_1$ can take any value from $1$ to $9$ ($9$ choices).The digits $x_2, x_3, x_4, x_5, x_6$ can each take any value from $0$ to $9$ ($10$ choices each).For any fixed values of $x_1, x_2, x_3, x_4, x_5, x_6$,the sum $S = x_1 + x_2 + x_3 + x_4 + x_5 + x_6$ is either even or odd.If $S$ is even,then $x_7$ must be even $(0, 2, 4, 6, 8)$ to make the total sum even ($5$ choices).If $S$ is odd,then $x_7$ must be odd $(1, 3, 5, 7, 9)$ to make the total sum even ($5$ choices).In either case,there are exactly $5$ choices for $x_7$ to ensure the sum of all digits is even.Therefore,the total number of such seven-digit numbers is $9 	imes 10 	imes 10 	imes 10 	imes 10 	imes 10 	imes 5 = 4500000$.

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

Similar Questions

The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

The number of shortest paths from point $A$ to $D$ (as shown in the figure) is:

In how many different ways can the letters of the word '$CORPORATION$' be arranged so that the vowels always come together?

It is required to seat $5$ men and $4$ women in a row so that the women occupy the even places. How many such arrangements are possible?

Let the eleven letters $A, B, \dots, K$ denote an arbitrary permutation of the integers $(1, 2, \dots, 11)$. Then, the product $(A - 1)(B - 2)(C - 3) \dots (K - 11)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module