SOLUTION: In the laboratory analysis of samples from a chemical
process, five samples from the process are analyzed daily. In
addition, a control sample is analyzed two times each day to
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process, five samples from the process are analyzed daily. In
addition, a control sample is analyzed two times each day to
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Question 1152123: In the laboratory analysis of samples from a chemical
process, five samples from the process are analyzed daily. In
addition, a control sample is analyzed two times each day to
check the calibration of the laboratory instruments.
(a) How many different sequences of process and control
samples are possible each day? Assume that the five
process samples are considered identical and that the two
control samples are considered identical.
(b) How many different sequences of process and control
samples are possible if we consider the five process samples
to be different and the two control samples to be identical?
(c) For the same situation as part (b), how many sequences
are possible if the first test of each day must be a control
sample?
a.
b.
c. ... It is said to be 6!. But, how's that possible? I need clarification for this Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website! Regarding part (c), because the control samples are considered identical, and the first sample must be a control, that leaves one control and 5 distinct process samples, resulting in 6! possible arrangements.
{CC} = control
{DEFGH} = process
C { DEFGHC }
^^^^^^
6! ways to arrange these
