(D) The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$

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

(D) The number of ways to arrange $r$ objects out of $n$ distinct objects is given by the permutation formula $^nP_r = \frac{n!}{(n-r)!}$.Here,$n = 5$ (vacant seats) and $r = 3$ (passengers).Therefore,the number of ways is $^5P_3 = \frac{5!}{(5-3)!} = \frac{5 \times 4 \times 3 \times 2!}{2!} = 5 \times 4 \times 3 = 60$.

Class 11 Mathematics Permutations and Combinations Definition of permutation, Number of permutations with or without repetition, Conditional permutations

Difficult

In a train,five seats are vacant. In how many ways can three passengers sit?

A
$20$
B
$30$
C
$10$
D
$60$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Permutations and Combinations

Subtopic

Definition of permutation, Number of permutations with or without repetition, Conditional permutations

$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is:

Medium

View Solution

How many arrangements can be made using the letters of the word $CALCUTTA$?

Easy

View Solution

What is the number of permutations of three letters $A, B, C$ taken all at a time?

Easy

View Solution

The number of all possible three-letter words that can be formed by choosing three letters from the letters of the word $FEBRUARY$ so that a vowel always occupies the middle place is:

DifficultTS EAMCET 2025

View Solution

The number of integers,greater than $7000$,that can be formed using the digits $3, 5, 6, 7, 8$ without repetition is:

MediumJEE MAIN 2023

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

In a train,five seats are vacant. In how many ways can three passengers sit?

Similar Questions

$4$ buses run between Bhopal and Gwalior. If a man goes from Gwalior to Bhopal by a bus and comes back to Gwalior by a different bus,then the total number of possible ways is:

How many arrangements can be made using the letters of the word $CALCUTTA$?

What is the number of permutations of three letters $A, B, C$ taken all at a time?

The number of all possible three-letter words that can be formed by choosing three letters from the letters of the word $FEBRUARY$ so that a vowel always occupies the middle place is:

The number of integers,greater than $7000$,that can be formed using the digits $3, 5, 6, 7, 8$ without repetition is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module