The value of \(\rm \dfrac{n!(n-1)!}{(n+1)!}\) is equal to:

  1. \(\rm \dfrac{n(n+1)!}{(n-1)}\)
  2. n(n-1)!
  3. (n!)2
  4. \(\rm \dfrac{(n-1)!}{(n+1)}\)

Answer (Detailed Solution Below)

Option 4 : \(\rm \dfrac{(n-1)!}{(n+1)}\)
Free
Army Havildar SAC - Quick Quiz
1.9 K Users
5 Questions 10 Marks 6 Mins

Detailed Solution

Download Solution PDF

Concept:

  • The factorial (n!) is defined as the product of first n natural numbers.
  • n! = n × (n - 1) × (n - 2) × … × 2 × 1.

 

Calculation:

We know that (n + 1)! = (n + 1) × n × (n - 1) × (n - 2) × ... × 2 × 1 = (n + 1) × n!.

\(\rm \therefore \dfrac{n!(n-1)!}{(n+1)!}=\dfrac{n!\times (n-1)!}{(n+1)\times n!}=\dfrac{(n-1)!}{n+1}\).

Latest Army Havildar SAC Updates

Last updated on Jun 11, 2025

-> The Indian Army has released the official notification for the post of Indian Army Havildar SAC (Surveyor Automated Cartographer).

-> Interested candidates had applied online from 13th March to 25th April 2025.

-> Candidates within the age of 25 years having specific education qualifications are eligible to apply for the exam.

-> The candidates must go through the Indian Army Havildar SAC Eligibility Criteria to know about the required qualification in detail. 

More Permutations and Combinations Questions

Get Free Access Now
Hot Links: teen patti casino download teen patti royal - 3 patti teen patti master apk teen patti rules teen patti master plus