Combinatorics

Combinatorics.
Combinatorics.

Combinatorics. Photo by autaro

ASQ Six Sigma Black Belt Exam Questions

Question:When a team consists of five black belts and eight quality engineers, how many unique meetings could be held consisting of one black belt and two quality engineers? Taken from (ASQ sample Black Belt exam.)

(A) 40
(B) 80
(C) 140
(D) 280

Answer: 140.

This question requires 2 sets of computations. First we want to calculate the number of combinations that exist with 8 Quality Engineers (QE) taken 2 at a time. Then we want to calculate the number of combinations that exist with 5 Black Belts (BB) taken 1 at a time.

8 QE taken 2 at a time = (n!) / k! (n-k)!   where n=8 and k=2.

(n!) / k! (n-k)! = (8!) / 2! (8-2)! = (8!) / 2! * 6!  = 28.

5 BB taken 1 at a time = (n!) / k! (n-k)!   where n=5 and k=1.

(n!) / k! (n-k)! = (5!) / 1! (5-1)! = (5!) / 1! * 4!  = 5.

Then we multiply both sets together: 28 * 5 = 140.

 

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