(A) We know that $_{n-1}P_r = \frac{(n-1)!}{(n-r-1)!}$ and $_{n-1}P_{r-1} = \frac{(n-1)!}{(n-r)!}$.Substituting these into the expression:$_{n-1}P_r +

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

(A) We know that $_{n-1}P_r = \frac{(n-1)!}{(n-r-1)!}$ and $_{n-1}P_{r-1} = \frac{(n-1)!}{(n-r)!}$.Substituting these into the expression:$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \frac{(n-1)!}{(n-r-1)!} + r \cdot \frac{(n-1)!}{(n-r)!}$$= \frac{(n-1)! \cdot (n-r)}{(n-r)!} + \frac{r \cdot (n-1)!}{(n-r)!}$$= \frac{(n-1)!}{(n-r)!} \cdot (n - r + r)$$= \frac{(n-1)! \cdot n}{(n-r)!}$$= \frac{n!}{(n-r)!} = _nP_r$

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

Difficult

$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \dots$

A
$_nP_r$
B
$_{n-1}P_r$
C
$_nP_{r-1}$
D
$2 \cdot _nP_r$

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 number of five-digit numbers divisible by $5$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition is

DifficultTS EAMCET 2011

View Solution

How many numbers greater than $24000$ can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

Medium

View Solution

In how many ways can $5$ prizes be distributed among four students when every student can take one or more prizes?

Easy

View Solution

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

Easy

View Solution

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if there are always $4$ letters between $P$ and $S$?

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

$_{n-1}P_r + r \cdot (_{n-1}P_{r-1}) = \dots$

Similar Questions

The number of five-digit numbers divisible by $5$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ without repetition is

How many numbers greater than $24000$ can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

In how many ways can $5$ prizes be distributed among four students when every student can take one or more prizes?

How many numbers greater than $100$ and divisible by $5$ can be made from the digits $3, 4, 5, 6$,if no digit is repeated?

In how many ways can the letters of the word $PERMUTATIONS$ be arranged if there are always $4$ letters between $P$ and $S$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module