(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 →

Find the number of $4$ letter words,with or without meaning,which can be formed out of the letters of the word $ROSE$,where the repetition of the letters is not allowed.

Easy

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

While dialing a telephone number,an old man forgets the last two digits,remembering only that these are different. If he dials the last two digits at random,what is the probability that the number is dialed correctly?

Easy

View Solution

The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

Easy

View Solution

In how many ways can the letters of the word $MAXIMA$ be arranged such that all vowels are together and all consonants are together?

EasyAP EAMCET 2021

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

Find the number of $4$ letter words,with or without meaning,which can be formed out of the letters of the word $ROSE$,where the repetition of the letters is not allowed.

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 $n$?

While dialing a telephone number,an old man forgets the last two digits,remembering only that these are different. If he dials the last two digits at random,what is the probability that the number is dialed correctly?

The number of $3$ digit odd numbers that can be formed by using the digits $1, 2, 3, 4, 5, 6$ when the repetition of digits is allowed is:

In how many ways can the letters of the word $MAXIMA$ be arranged such that all vowels are together and all consonants are together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module