(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 →

How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

View Solution

If all the letters of the word $MOST$ are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order,then the rank of the word $STOM$ when counted from the rank of the word $MOST$ is:

MediumTS EAMCET 2025

View Solution

If all the words formed by using the letters of the word $CRICKET$ are arranged in a dictionary in alphabetical order,how many words appear before the word $CRICKET$?

Difficult

View Solution

Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

Medium

View Solution

Ten men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

EasyTS EAMCET 2013

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

How many permutations can be made by using all the letters of the word $MATHEMAGICA$?

If all the letters of the word $MOST$ are permuted and the words (with or without meaning) thus obtained are arranged in the dictionary order,then the rank of the word $STOM$ when counted from the rank of the word $MOST$ is:

If all the words formed by using the letters of the word $CRICKET$ are arranged in a dictionary in alphabetical order,how many words appear before the word $CRICKET$?

Let $n$ be a number of digits. Using the three digits $2, 5, 7$,at least $900$ distinct $n$-digit numbers can be formed. What is the minimum value of $n$?

Ten men and $6$ women are to be seated in a row so that no two women sit together. The number of ways they can be seated is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module