September 28, 2010
Math 351  Test 1
1. Suppose we have
five
identical
red books,
six
identical
green books, and
three
different
yellow books.
(a) In how many different ways can they be arranged on a shelf?
(b) In how many different ways can they be arranged on a shelf if the yellow books must all be
together?
2. Suppose we have
five
different math books,
seven
different chemistry books, and
five
different physics
books. In how many ways can we select
three
books from each of the three subjects and then arrange
those nine selected books on a shelf in such a way that books of the same subject are kept together?
3. How many ways can we divide
ten
identical desks among
six
schools, assuming that not every school
has to be given a desk.
(I suggest you begin by letting
x
i
be the number of desks given to school
i
, where
i
varies from
1
to 6.)
4. Let
A
and
B
be two events.
Suppose in this question that
P
(
A
) = 3
/
12
and
P
(
B
) = 5
/
12.
Suppose also the probability of the event that either
A
or
B
occurs is
7
/
12.
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 Spring '08
 Moumen,F
 Math, Probability

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