(D) To form a $6$-digit number using the digits $3, 1, 7, 0, 9, 5$,we must ensure the first digit is not $0$.Total permutations of $6$ distinct digits

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

(D) To form a $6$-digit number using the digits $3, 1, 7, 0, 9, 5$,we must ensure the first digit is not $0$.Total permutations of $6$ distinct digits is $6! = 720$.If the first digit is $0$,the remaining $5$ positions can be filled by the remaining $5$ digits in $5!$ ways.$5! = 120$.Therefore,the number of $6$-digit numbers that do not start with $0$ is $6! - 5! = 720 - 120 = 600$.

Competitive Quantitative Aptitude Permutation and Combination Permutation and Combination

Medium

How many different numbers of $6$ digits can be formed with the digits $3, 1, 7, 0, 9, 5$?

A
$500$
B
$400$
C
$480$
D
$600$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Permutation and Combination

Subtopic

Permutation and Combination

How many arrangements can be made of the letters of the word '$ARRANGEMENT$'?

Medium

View Solution

How many $3$-digit numbers can be formed by using the digits $1, 3, 6,$ and $8$,when the digits may be repeated any number of times?

Easy

View Solution

The number of arrangements of the letters of the word $CALCUTTA$ is:

Easy

View Solution

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?

Medium

View Solution

How many $3$-digit numbers can be formed using $0, 2, 3, 5, 7$ when repetition is allowed?

Medium

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

How many different numbers of $6$ digits can be formed with the digits $3, 1, 7, 0, 9, 5$?

Similar Questions

How many arrangements can be made of the letters of the word '$ARRANGEMENT$'?

How many $3$-digit numbers can be formed by using the digits $1, 3, 6,$ and $8$,when the digits may be repeated any number of times?

The number of arrangements of the letters of the word $CALCUTTA$ is:

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when$(i)$ repetition of digits is not allowed(ii) repetition of digits is allowed?

How many $3$-digit numbers can be formed using $0, 2, 3, 5, 7$ when repetition is allowed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module

How many $3$-digit odd numbers can be formed from the digits $1, 2, 3, 4, 5, 6$ when
$(i)$ repetition of digits is not allowed
(ii) repetition of digits is allowed?