Question

If in a group of n distinct objects, the number of arrangements of 4 objects is 12 times the number of arrangements of 2 objects, then the number of objects is

• A. 10
• B. 8
• C. 6
• D. None of these

Answer 1

The correct option is C

6

According to the question :

${}^n{P}_4=12\times {}^n{P}_2$

$\Rightarrow \frac{n!}{(n-4)!}=12\times \frac{n!}{(n-2)!}$

$\Rightarrow \frac{(n-2)!}{(n-4)!}=12$

$\Rightarrow (n-2)(n-3)=4\times 3$

$\Rightarrow$ n-2 = 4

$\Rightarrow$ n=6