Twelve employees of a company are being assigned to offices

Twelve employees of a company are being assigned to offices. There are four offices and each is large enough for three people. How many ways are there to assign employees to offices?

Solution

Here our task is

1) divide 12 employee into groups of 3

2)select which group is assigned which office,

hence number of ways of dividing 12 employee into 4 groups of 3 employee = 12 C3 * 9C3*6C3*3C3 =

369600

now groups are made,but wehave to decide offices for each group ,which is nothing but 4! = 24

so total ways to assign employees to offices = 369600 *24 = 8870400