Question

11. In a group of boys the number of arrangement of 4 boys is 12 times the number
arrangements of 2 boys. The number of boys in the
group
is
(a) 10
(b) 8​

Answer 1

Let the number of boys be x.

=> xP4 = 12*xP2

=> x!/(x-4)! = 12*x!/(x-2)!

=> (x-2)!/(x-4)! = 12

=> (x-2)(x-4) = 12

=> x^2-5x-6 = 0

=> (x-6)(x+1) = O

=> x = 6

Therefore ,

The number of boys in the group is 6.

Hope It Helps (: