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