AMS
301
SECOND
TEST
Test
A
Fall,
2009
1.
Find
the
coefficient
of
x^24
in
(x^3+
x^4+
x^5+
x^6)^5.
2. Consider the problem of counting the ways to select 25 objects from 6 types with at least two
objects
of
each
type.
a) Model this problem as an integersolutionofequationproblem.(BR> b) Model this problem as
a
certain
coefficient
of
a
generating
function.
c)
Solve
this
problem.
3. Find the probability that 4card hand (from a 52card deck) has no pair each card of a different
kind).
4. How many 6digit decimal sequences are there with exactly
r
3's.
5. How many arrangements of MATHEMATICAL are there in which ME appear together but ME
is
not
immediately
followed
by
an
A
(no
MEA)?
6. How many arrangements of letters in ORIGINATING have ALL of the following pr operties:
(i) at least two letters between each I, (ii) begins or ends (not both) with an I, and (iii) the
consonants
are
in
alphabetical
order.
7. You have 6 friends. How many ways are there to invite a different subset of two of these friends
over
for
dinner
on
5
successive
nights.
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 Spring '08
 ARKIN
 Vowel, Consonant, Dr. Tucker, x^3+ x^4+ x^5+

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