Katie has 9 employees that she must assign to 3 different pr

BTGmoderatorDC wrote:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations of project assignments are possible?

A. 252
B. 1,680
C. 2,340
D. 362,880
E. 592,704

OA B

Source: Princeton Review

Number of ways Katie can assign any 3 employees to the first project = 9C3 = (9.8.7)/(1.2.3) = 84;

Number of ways Katie can assign any 3 employees to the second project = 6C3 = (6.5.4)/(1.2.3) = 20; since out of 9 employees, 3 are assigned to the first project, only 6 employees are remaining for the selection

Number of ways Katie can assign any 3 employees to the third project = 3C3 = 1

Total number fo ways = 84*20*1 = 1,680

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations of project assignments are possible?

A. 252
B. 1,680
C. 2,340
D. 362,880
E. 592,704

OA B

Source: Princeton Review

The first 3 employees can be selected in 9C3 = (9 x 8 x 7)/3! = 3 x 4 x 7 = 84 ways.

The next 3 employees can be selected in 6C3 = (6 x 5 x 4)/3! = 20 ways.

The final 3 employees can be selected in 3C3 = 1 way.

Therefore, the total number of ways the 3 projects can be assigned is:

84 x 20 x 1 = 1,680

Answer: B