This preview shows pages 1–2. Sign up to view the full content.
2.1.5.
(a)
There
are
C!.r:4
waln of picking
depdrtments.
For
depart_
ment choices
berow,
.'"
iil
trr" t"i'.r
;;;;".
of commitees
from
those
de.
partments,
by using
the counting
;;tr.;l;,
{1,2,3}
:.4
._4
.5
:
8oi
{t,2,4}
:
4. 4
.5
:
8oi
{1,3,4}
:
4.
s.5
:
roo;
ii,i,nl
:
4. 5.5
:
1oo.
ilTj"j$:tmber
of possible
committees
is then
the sum
80 + 80
+
100
+
(b)
The committe
conditions.
r,o.
"*u.il]enot.equally
lil,ely
under
the specified
selection
parrment
2,
an
d,
i.':ii'
j:,
r:::ff
"l "r*:F"1",T:ffi**"
t,:
5
i$:Iil:ilrc3mbination'
,r'""
."r".;
;*
three
indiviiuui,"io*
,r,oru
P[z from
departmt
'"'
t:'*1?T.Tiif:*J
2,
z
rromdepartment
3l
But for
the other
department"""ri,o,l*l"r*
*
P[r from
department
l, y
from
departme
:
l

rl
.
t.:r
"tf
2'z
from
department
4J
4 \4
L s)_Tfr.
P[z from department
1,
9,fr9T department
3, z from department
4l
C/i*
I
pfc
from denarrman+
,
".1]i
:t
+' =
#,
ar
ot4,
efl#w3
Tllbf/?+kt
.
/lt'
t,/
o?+/z
ry{+}4/f
Ui1Ua"rl
d4a/^
ter
t
P[c from
department
2,
y
from
departn
rndividua,sd**h;;;i,i,:,:t'tt':::il.:":"T::,:,,
multiply
the probabititv
i/+ rr,.i1i"'ai"l
abilitv
i n
at
t
r,e in
a..,i
q
u
"r'
t
"
il"
o'"o''";11:"',",
:'u
jj
$iji
lo:
rl"r*
3;f;I*"
I
and 2' Uut
oo'rviziiJ.l.o"',*ents
3 and
4.
(3/16 vs.
,
x
I
2.L.25. Assume that the fifteea
subjects are indistinguishable
The prob
since this is a bit
less than 8%, we have
a little evidence
that brand selec'
lem is to couut tbe number of
ways that 15 such subjects,
positioned in
a row,
ca' be split into 3 goups.
As in
Fig'
2'2, do tbe
partitioning
l/,0 f
,
"
by inserting two special
markers into the
list aaywhere. Then
there
are
'.'",,:6.
fS + Z
=
1?
positions in the new list, and a
partition correspol&
"iiqY*
ifnff8:'"]:
to a
selection of 2 positions
for the markeis'
wbich can
e o"TrTrfil
ways. Now let
us count the number of ways
in which at
least l2 of the
rJ;**
are in the first category,
ie.
they prefer brand
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Moumen,F
 Counting

Click to edit the document details