(C) We know that the formula for permutation is $^nP_r = \frac{n!}{(n-r)!}$.Consider the expression $(n - r + 1) \times ^nP_{r - 1}$.Using the formula

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

(C) We know that the formula for permutation is $^nP_r = \frac{n!}{(n-r)!}$.Consider the expression $(n - r + 1) \times ^nP_{r - 1}$.Using the formula,$^nP_{r-1} = \frac{n!}{(n - (r - 1))!} = \frac{n!}{(n - r + 1)!}$.Substituting this into the expression:$(n - r + 1) \times \frac{n!}{(n - r + 1)!} = (n - r + 1) \times \frac{n!}{(n - r + 1) \times (n - r)!}$.Canceling the term $(n - r + 1)$ from the numerator and denominator:$= \frac{n!}{(n - r)!} = ^nP_r$.Thus,the correct option is $C$.

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

Difficult

$(n - r + 1) \times ^nP_{r - 1} = \dots$

A
$^{n-1}P_r$
B
$^{n+1}P_r$
C
$^nP_r$
D
$^nP_{r+1}$

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

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

Easy

View Solution

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

View Solution

If all the words with or without meaning made using all the letters of the word $KANPUR$ are arranged as in a dictionary,then the word at $440^{th}$ position in this arrangement is:

DifficultJEE MAIN 2025

View Solution

The letters of the word $COCHIN$ are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word $COCHIN$ is

DifficultIIT 2007

View Solution

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

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

$(n - r + 1) \times ^nP_{r - 1} = \dots$

Similar Questions

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

Six objects $O_1$ to $O_6$ are arranged one on top of the other. In how many ways can these be arranged such that $O_1$ and $O_2$ are the $2$ bottom-most objects?

If all the words with or without meaning made using all the letters of the word $KANPUR$ are arranged as in a dictionary,then the word at $440^{th}$ position in this arrangement is:

The letters of the word $COCHIN$ are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word $COCHIN$ is

How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Vedclass Test Series

Exam Paper Generator

Online Exam Module