(C) $5$-digit number cannot start with $0$. Total permutations of $5$ distinct digits taken all at once is $^5P_5 = 5! = 120$. Numbers starting with $

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

(C) $5$-digit number cannot start with $0$. Total permutations of $5$ distinct digits taken all at once is $^5P_5 = 5! = 120$. Numbers starting with $0$ are formed by arranging the remaining $4$ digits in the last $4$ positions,which is $^4P_4 = 4! = 24$. Therefore,the number of $5$-digit numbers is $120 - 24 = 96$.

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

Difficult

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

AP EAMCET 2001 All AP EAMCET

TS EAMCET 2001 All TS EAMCET

A
$16$
B
$24$
C
$96$
D
$120$

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

Previous Year

AP EAMCET 2001 Paper All AP EAMCET years →

Previous Year

TS EAMCET 2001 Paper All TS EAMCET years →

The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:

DifficultJEE MAIN 2026

View Solution

Out of $10$ persons,$A, B$,and $C$ are to speak at a function. If $A$ wants to speak before $B$ and $B$ wants to speak before $C$,in how many ways can they speak?

Medium

View Solution

There are $3$ applicants for a scholarship in Physics,$5$ for Mathematics,and $4$ for Chemistry. In how many different ways can these scholarships be awarded such that at least one scholarship is awarded in each subject?

Medium

View Solution

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

EasyAP EAMCET 2022

View Solution

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

DifficultJEE MAIN 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

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

Similar Questions

The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:

Out of $10$ persons,$A, B$,and $C$ are to speak at a function. If $A$ wants to speak before $B$ and $B$ wants to speak before $C$,in how many ways can they speak?

There are $3$ applicants for a scholarship in Physics,$5$ for Mathematics,and $4$ for Chemistry. In how many different ways can these scholarships be awarded such that at least one scholarship is awarded in each subject?

How many words,with or without meaning,each of $2$ vowels and $3$ consonants can be formed from the letters of the word $DAUGHTER$?

The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module