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

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 

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