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Generalized Bernouli Trials
Consider the collection of all possible
sequences of A’s, B’s
and
C’s, in which there are 3 A’s, 2 B’s, and 5C’s.
Two examples of
such sequences are shown below.
ACABCCBACC
CBABAACCCC
We want to answer the question, “how many different such
sequences are there?”
To answer this question we first consider a different, but related
question.
Suppose that we number the A’s from 1 to 3, the B’s
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numbered
sequences of the letters.
Examples of such numbered
sequences are:
A
2
C
1
A
1
B
2
C
4
C
5
B
1
A
3
C
2
C
3
C
2
B
2
A
1
B
1
A
3
A
2
C
4
C
3
C
5
C
1
How many different
numbered
sequences of 3 A’s, 2 B’s, and 5C’s
are there?
Since the numbering operation results in 10 completely
distinct (distinguishable) objects,
there are just 10! (10 factorial)
different permutations of their ordering, so there are 10! Different
numbered
sequences.
Next, consider the following procedure for constructing a
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 Spring '11
 voltz

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