CS336f1016 - 11/8/10 Example


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Unformatted text preview: 11/8/10 Example
 How
many
ways
are
there
of
arranging
6
people
 at
a
round
table?
 How
many
ways
are
there
of
arranging
six
 people
at
a
round
table
so
that
Romeo
and
 Juliet
are
sitting
next
to
one
another
but
 Ceasar
and
Brutis
are
not?
 Example
 •  How 
 many 
 ways 
 can 
 we 
 order 
 the 
 letters 
 in
 MISSISSIPPI
where
all
four
I’s
are
not
together?
 
 How
is
this
different
from
past
problems?
 Example
 How
many
ways
can
you
roll
a
pair
of
red
dice?
 Example
 How
many
ways
can
you
roll
a
pair
of
red
dice?
 11 12 22 13 23 33 14 24 34 44 15 25 35 45 55 16 26 36 46 56 66 Table
 Our
questions:
 order replacement yes no yes no Example
 How
many
ways
can
you
place
two
balls
in
three
 boxes?
 Product rule Permutation ? Combination 1 11/8/10 Example
 How
many
ways
can
you
place
two
balls
in
three
 boxes?
 1 1 1 1 1 1 2 2 2 Example
 How
many
ways
can
you
place
two
balls
in
 three
boxes?
 1 1 1 1 1 2 2 2 *|*|
 
 
 
 **||
 *||*
 
 
 
 |**|
 1 |*|*
 
 
 
 ||**
 Example
 How
many
ways
can
you
place
two
balls
in
 three
boxes?

How
many
ways
can
we
 choose
places
for
two
balls
and
two
 transitions”

C(4,2)=6
 *|*|
 
 
 
 **||
 *||*
 
 
 
 |**|
 |*|*
 
 
 
 ||**
 Our
questions:
 order replacement yes no Table
 Yes Product rule Product rule P(n,r) No Combination C(n+r-1,r) C(n,r) Example
 
 A 
 bagel 
 shop 
 has 
 onion 
 bagels, 
 poppy 
 seed
 bagels, 
 egg 
 bagels, 
 pumpernickel 
 bagels, 
 salty
 bagels, 
 sesame 
 seed 
 bagels, 
 raisin 
 bagels, 
 and
 plain
bagels.


 •  How 
 many 
 ways 
 are 
 there 
 of 
 choosing 
 six
 bagels?
 Example
 
 A
bagel
shop
has
onion
bagels,
poppy
seed
 bagels,
egg
bagels,
pumpernickel
bagels,
salty
 bagels,
sesame
seed
bagels,
raisin
bagels,
and
 plain
bagels.


 •  How
many
ways
are
there
of
choosing
a
dozen
 bagels?
 2 11/8/10 Example
 
 A
bagel
shop
has
onion
bagels,
poppy
seed
 bagels,
egg
bagels,
pumpernickel
bagels,
salty
 bagels,
sesame
seed
bagels,
raisin
bagels,
and
 plain
bagels.


 •  How
many
ways
are
there
of
choosing
a
dozen
 bagels
with
at
least
one
of
each
kind?
 Example
 
 A
bagel
shop
has
onion
bagels,
poppy
seed
 bagels,
egg
bagels,
pumpernickel
bagels,
salty
 bagels,
sesame
seed
bagels,
raisin
bagels,
and
 plain
bagels.


 •  How
many
ways
are
there
of
choosing
a
dozen
 bagels
with
at
least
3
plain?
 Example
 
 A
bagel
shop
has
onion
bagels,
poppy
seed
 bagels,
egg
bagels,
pumpernickel
bagels,
salty
 bagels,
sesame
seed
bagels,
raisin
bagels,
and
 plain
bagels.


 •  How
many
ways
are
there
of
choosing
a
dozen
 bagels
with
less
than
3
plain?
 Example
 
 A
bagel
shop
has
onion
bagels,
poppy
seed
bagels,
 egg
bagels,
pumpernickel
bagels,
salty
bagels,
 sesame
seed
bagels,
raisin
bagels,
and
plain
bagels.


 •  How
many
ways
are
there
of
choosing
a
dozen
bagels
 with
at
least
3
plain
and
no
more
than
2
onion?
 Example
 •  How
many
positive
numbers
less
than
1000
 have
at
least
one
digit
equal
9
and
the
sum
of
 the
digits
equal
13.
 3 ...
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This note was uploaded on 11/30/2010 for the course CS 336 taught by Professor Myers during the Fall '08 term at University of Texas at Austin.

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