Probability example question: How do you do this in nCr or nPr?

Question

A firm is going to create three teams of four from twelve employees. How many ways can the twelve employees be selected for the three teams?

A)34,650.

B)1,320.

C)495.

Explanation: This problem is a labeling problem where the 12 employees will be assigned one of three labels. It requires the labeling formula. There are [(12!) / (4! × 4! × 4!)] = 34,650 ways to group the employees.

(Study Session 2, Module 8.3, LOS 8.o)

mikey · Answer

You use nCr for this:

nCr = n! / ((n – r)! r!)

Creating 3 teams of 4 from 12 employees:

For team A, you choose 4 out of 12 employees:

12C4 = 12 choose 4 = 12! / ((12-4)! 4!) = 495 scenarios (calculate using BA II Plus)

For team B, you choose 4 out of 8 employees:

8C4 = 8 choose 4 = 8! / ((8-4)! 4!) = 70 scenarios

For team C, there's only one scenario since it's all the unchosen people.

For all possible combinations, multiply A * B * C = 495 * 70 * 1

= 34,650 combinations

pcunniff · Answer

thanks Mikey - how do you get the 8NCR4? Order matters for NCR and doesnt for NPR, correct? Get confused with this. I understand the first part, but unsure of where you get 8NCR4.

Patrick