UMBC CMSC203 Discrete Structures, Section 06, Spring 2016
Homework 10, Due Thursday, 04/21
For each of these questions, you must show your work and explain
your answer.
You will have to write down some English sentences.
Answers that consist of a single number will receive
less than 50% credit!
When factorials are involved, leave your answer in terms of factorials
(e.g., 5!/(3! ⋅ 2)).
- Trip Planning. For a trip, you packed 2 pairs of
sneakers, 3 pairs of jeans, 4 pairs of shorts, 5 shirts, 2 sweaters
and 3 rings. How many different outfits can you make from the
clothing you packed, if an "outfit" consists of 1 pair of sneakers,
1 pair of jeans or shorts (but not both), 1 shirt, at most 1 sweater
and any number of rings? (Note: wearing rings on different fingers
does not count as a different "outfit.")
Note: Assume that your sneakers, jeans, shorts, shirts,
sweaters and rings are distinguishable.
- Sock Drawer.
Suppose your sock drawer has 17 pairs of socks that are black, white
or tan. Which of the following statements must be true? Justify
your answer.
- There are at least 5 pairs of black socks, at least 5
pairs of white socks and at least 5 pairs of tan socks.
- There are at most 4 pairs of black socks, at most 4 pairs
of white socks or at most 4 pairs of tan socks.
- There are at least 6 pairs of black socks, at
least 6 pairs of white socks or at least 6 pairs of tan
socks.
- Another Sock Drawer.
Suppose that your sock drawer has 6 pairs of black socks, 5 pairs of
white socks and 6 pairs of tan socks. How many different ways are there to
pack 5 pairs of socks? You can bring as many pairs of socks of each color
as you want. Assume that socks of the same color are not
distinguishable.
- Hotel Room Closet.
In the hotel room, you hang up in the closet the 5 shirts and 2
sweaters that you packed. How many ways can you arrange the shirts
and sweaters in the closet (from left to right) so that the 2
sweaters are adjacent to each other? (As before, assume that your
shirts and sweaters are distinguishable.)
Last Modified:
14 Apr 2016 12:22:22 EDT
by
Richard Chang
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