Question

If ⁿP₃= ⁿP₂, then find the value of n.
1. 3
2. 7
3. 9
4. 5

Answer 1

Correct Answer - Option 1 : 3

Concept Used: 

Factorial Notation:

Let n be a positive integer. Then, factorial n, denoted n! is defined as :

n! = n × (n - 1) × (n - 2) ... 3 × 2 × 1 

The different arrangements of a given number of things by taking some or all at a time, are called permutations. 

Formula Used:

Number of Permutations:

Number of all permutations of n things, taken r at a time, is given by :

nPr = n!/(n - r)!

Calculations:

nP3= nP2

⇒  n!/(n - 3)! =  n!/(n - 2)!

⇒  1/(n - 3)! =  1/(n - 2)!

⇒  (n - 2)! =  (n - 3)!

⇒  (n - 2)  × (n - 3)!=  (n - 3)!

⇒  (n - 2) =  1

⇒  n =  3