Question 660952: In an experiment involving a treatment applied to 6 test subjects, researchers plan to use a simple random sample of 6 subjects selected from a pool of 8 available subjects. How many different random samples are possible?
A.210
B.250
C.28
D.7776
Answer by jim_thompson5910(35256)   (Show Source):
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In an experiment involving a treatment applied to 6 test subjects, researchers plan to use a simple random sample of 6 subjects selected from a pool of 8 available subjects. How many different random samples are possible?
A.210
B.250
C.28
D.7776
Here's why the answer is choice C.
You have 8 choices for the first slot, 7 for the second, 6 for the 3rd, 5 for the 4th, 4 for the 5th, and 3 for the 6th
So if order matters, then you have 8*7*6*5*4*3 = 20,160 different ways to choose 6 people from a pool of 8.
But order doesn't matter, so you have to divide by 6! = 6*5*4*3*2*1 = 720 to get
20160/720 = 28
So there are 28 random samples.
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