Question

In how many ways can 12 persons be divided into 3 group of 4 each .........................
Options are:
A)12!/4!*3
B)(12!*3!*3)/4!*3
C)12!
D)None of the above.

Answer 1

12 people and 3 groups of 4
no. of ways to select 4 people from 12 for first group = 12C4 = 495
no. of ways to select 4 people from remaining 8 for second group = 8C4 = 70
no. of ways to select 4 people from 4 for third group = 4C4 = 1

total no. of ways to select people for group = 495 * 70 * 1 / 3! = 34650 /6

= 5775
Here we divide by 3! here position or identification of groups does not matter.
All groups have equal identity, arrangement of group does not matter.
For example, if there are 3 groups having names G1, G2, G3 then there is no need to divide by 3!.