In a set of 15 aluminum castings, two castings are defective (D), and the remaining thirteen are good (G).A quality control inspector randomly selects three of the fifteen castings without replacement and classifies each as defective (D)or good (G).How large is the sample space?
A)3,375
B)2,730
C)455
D)15
E)3

Question

Quizplus · Accepted Answer

The sample space in this scenario is the total number of possible ways the inspector can select three castings out of the 15 available castings. This can be calculated using the combination formula: 
nCr = n! / r!(n-r)!
Where n = 15 and r = 3. 
Plugging in the values, we have:
15C3 = 15! / 3!(15-3)! = 455
Therefore, the sample space consists of 455 possible outcomes.

In a Set of 15 Aluminum Castings, Two Castings Are