Question 774680: A student takes a test consisting of 5 questions. For each question, she must choose either A, B or C.
(a) How many possible ways are there for her to complete the test?
(b) How many of these possibilities include the answer A at least twice?
(c) How many possible ways are there to complete the test without ever giving the same
answer to two consecutive questions?
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! (a)
For each of the 5 questions, there are 3 ways to answer
The number of possible ways to do the test are:
(b)
Just looking at the A column for each of the 5 questions,
It will either have a check mark or no check mark.
The number of possible arrangements for the A
column are:
I can exclude
A( 0, 0 , 0, 0, 0 )
A( 1, 0, 0, 0, 0 )
A( 0, 1 , 0, 0, 0 )
A( 0, 0 , 1, 0, 0 )
A( 0, 0, 0, 1, 0 )
A( 0, 0 , 0, 0, 1 )
Excluding these 6 cases, that leaves
 with A appearing at least twice
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(c)
I need to exclude:
(1) A
(2) A
----
(2) A
(3) A
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(3) A
(4) A
----
(4) A
(5) A
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These 4 cases are excluded as well
as for B's and C's, so there are
 exclusions
 allowed
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