Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ..., 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer
Your crazy uncle has built a panic room in his basement. The panic room can only be accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ..., 6 and is 8 digits long. Because your uncle really is crazy, the numeric code must be monotone, meaning either always non-decreasing or always non-increasing. How many possible codes are there under these conditions? Your Answer: Answer
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 22E: License Plate Numbers In a certain state, each automobile license plate number consists of two...
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Discrete mathematics
Transcribed Image Text:Your crazy uncle has built a panic room in his basement. The panic room can only be
accessed by entering a numeric code. The code uses only the digits 0, 1, 2, ... , 6 and
is 8 digits long. Because your uncle really is crazy, the numeric code must be
monotone, meaning either always non-decreasing or always non-increasing. How
many possible codes are there under these conditions?
Your Answer:
Answer
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For example, using only the digits 0, 1, 2, 3: a 7-digit non-increasing code might be
3322210, or a 9-digit non-decreasing code might be 001123333. Each example could
be represented by a bar/star chart, where the stars represent using a particular digit
and the bars represent the transitions from one digit to the next. Count the number
of bar/star charts for possible non-increasing and possible non-decreasing codes,
then use the addition principle.
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