(B) The $1^{st}$ ring has $10$ digits $(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)$.The $2^{nd}$ ring has prime numbers greater than $2$ and less than $30$: ${3, 5

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

(B) The $1^{st}$ ring has $10$ digits $(0, 1, 2, 3, 4, 5, 6, 7, 8, 9)$.The $2^{nd}$ ring has prime numbers greater than $2$ and less than $30$: ${3, 5, 7, 11, 13, 17, 19, 23, 29}$. There are $9$ such numbers.The $3^{rd}$ ring has all vowels: ${a, e, i, o, u}$. There are $5$ such vowels.Total number of ways to set the lock $= 10 \times 9 \times 5 = 450$.Since there is only $1$ correct combination to open the lock,the total number of unsuccessful attempts $= 450 - 1 = 449$.

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

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

A
$405$
B
$449$
C
$499$
D
$501$

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

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:

DifficultAP EAMCET 2001

View Solution

There are $9$ chairs in a room,and $6$ people are to be seated. One of these chairs is a special chair reserved for a special guest. In how many ways can these people be seated?

Medium

View Solution

The number of $4$-letter words,with or without meaning,which can be formed using the letters of '$PQRPQRSTUVP$',is:

DifficultJEE MAIN 2026

View Solution

The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :

DifficultJEE MAIN 2023

View Solution

How many arrangements of the letters of the word $SALOON$ are there,such that the two $O$'s do not come together?

Easy

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

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.

Similar Questions

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:

There are $9$ chairs in a room,and $6$ people are to be seated. One of these chairs is a special chair reserved for a special guest. In how many ways can these people be seated?

The number of $4$-letter words,with or without meaning,which can be formed using the letters of '$PQRPQRSTUVP$',is:

The letters of the word $OUGHT$ are written in all possible ways and these words are arranged as in a dictionary,in a series. Then the serial number of the word $TOUGH$ is :

How many arrangements of the letters of the word $SALOON$ are there,such that the two $O$'s do not come together?

Vedclass Test Series

Exam Paper Generator

Online Exam Module