In a group of boys the number of arrangement of 4 boys is 12 times the number ofarrangements of 2 boys. The number of boys in the group is

Let's assume that the number of boys in the group is "x".

To find the number of arrangements of 4 boys, we use the formula for permutations, which is nPr = n! / (n-r)!. In this case, we have 4 boys, so the number of arrangements of 4 boys is 4P4 = 4! / (4-4)! = 4! / 0! = 4! = 24.

Similarly, the number of arrangements of 2 boys is 2P2 = 2! / (2-2)! = 2! / 0! = 2! = 2.

According to the given information, the number of arrangements of 4 boys is 12 times the number of arrangements of 2 boys. So, we can set up the equation:

24 = 12 * 2

Simplifying the equation, we get:

24 = 24

This equation is true for any value of "x". Therefore, the number of boys in the group can be any number.