If a group of `n` distinct objects, the number of arrangements of 4 object 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

Explanation

According to the question :

`n_(P_4)=12xxn_(P_2)`

`⇒(n!)/((n−4)!)=12×(n!)/((n−2)!)`

`⇒((n−2)!)/((n−4)!)=12`

`⇒(n−2)(n−3)=4xx3`

`⇒ n-2 = 4`

`⇒ n=6`