(A) The total number of $4$-digit numbers formed using $4$ distinct digits is $4! = 24$.Each digit appears in each place (units,tens,hundreds,thousand

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

(A) The total number of $4$-digit numbers formed using $4$ distinct digits is $4! = 24$.Each digit appears in each place (units,tens,hundreds,thousands) exactly $\frac{24}{4} = 6$ times.The sum of the digits is $2 + 4 + 6 + 8 = 20$.The sum of the digits in any given place is $6 \times 20 = 120$.Therefore,the sum of all such numbers is $120 \times 1 + 120 \times 10 + 120 \times 100 + 120 \times 1000$.$= 120(1 + 10 + 100 + 1000) = 120 \times 1111 = 133320$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Medium

The sum of all $4$-digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

A
$133320$
B
$533280$
C
$53328$
D
None of these

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutation and Combination

Subtopic

Definition of permutation, Number of permutations with or without repetition, Conditional permutations

How many $4$-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that at least one digit is $1$?

Medium

View Solution

If $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$,then $r = \dots$

Easy

View Solution

If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

Easy

View Solution

The number of six-letter words (with or without meaning) formed using all the letters of the word $VOWELS$ such that all the consonants never come together is ... .

EasyJEE MAIN 2021

View Solution

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ is:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The sum of all $4$-digit numbers that can be formed by using the digits $2, 4, 6, 8$ (repetition of digits not allowed) is

Similar Questions

How many $4$-digit numbers can be formed using the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that at least one digit is $1$?

If $\frac{^{56}P_{r+6}}{^{54}P_{r+3}} = 30800$,then $r = \dots$

If $^n{P_r} = 720 \times {^n{C_r}}$,then $r$ is equal to:

The number of six-letter words (with or without meaning) formed using all the letters of the word $VOWELS$ such that all the consonants never come together is ... .

The total number of $4$-digit numbers which can be formed using the digits $1, 2, 3, 4$ without repetition such that the digit $n+1$ never immediately follows the digit $n$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module