(C) To find the sum of the digits in the unit place,we fix one digit at the unit place.If we fix $3$ at the unit place,the remaining $3$ digits $(4, 5

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

(C) To find the sum of the digits in the unit place,we fix one digit at the unit place.If we fix $3$ at the unit place,the remaining $3$ digits $(4, 5, 6)$ can be arranged in the remaining $3$ positions in $3! = 6$ ways.Similarly,if we fix $4, 5,$ or $6$ at the unit place,each will appear in the unit place $3! = 6$ times.The sum of the digits in the unit place is $6 \times (3 + 4 + 5 + 6) = 6 \times 18 = 108$.

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

Easy

The sum of the digits in the unit place of all numbers formed with the help of $3, 4, 5, 6$ taken all at a time is

A
$18$
B
$432$
C
$108$
D
$144$

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

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

MediumKCET 2022

View Solution

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

View Solution

How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

Easy

View Solution

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ which are divisible by $3$,when repetition of digits is allowed any number of times,is

DifficultAP EAMCET 2017

View Solution

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

DifficultKVPY 2019

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 the digits in the unit place of all numbers formed with the help of $3, 4, 5, 6$ taken all at a time is

Similar Questions

If all permutations of the letters of the word $MASK$ are arranged in the order as in a dictionary,with or without meaning,which one of the following is the $19^{th}$ word?

If the permutations of $A, B, C, D, E$ taken all together are written down in alphabetical order as in a dictionary and numbered,then the rank of the permutation $DEBAC$ is

How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

The number of four-digit numbers that can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ which are divisible by $3$,when repetition of digits is allowed any number of times,is

The number of four-letter words that can be formed with letters $a, b, c$ such that all three letters occur is

Vedclass Test Series

Exam Paper Generator

Online Exam Module